Answer:
a) The null hypothesis is represented as
H₀: p ≥ 0.08
The alternative hypothesis is represented as
Hₐ: p < 0.08
b) A type I error for this question would be that
we conclude that the proportion of defective products is less than 8% when in reality, the proportion of defective products, is more than or equal to 8%.
c) At most, the number of defective products in the sample for you to agree to use the new product = 7
d) If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be (103, 497)
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and is usually stating the opposite of the theory is being tested. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing. It usually contains the signs ≠, < and > depending on the directions of the test
For this question, we want to prove that less than 8% of the products we subsequently purchase will be defective.
So, the null hypothesis will be that there is not enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective. That is, the proportion of the sample that are defective is more than or equal to 8%.
And the alternative hypothesis is that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective.
Mathematically,
The null hypothesis is represented as
H₀: p ≥ 0.08
The alternative hypothesis is represented as
Hₐ: p < 0.08
b) A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true. It involves saying that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective when in reality, there isn't enough evidence to arrive at this conclusion.
That is, the proportion of defective products in reality, is more than or equal to 8% and we have concluded that the proportion is less than 8%.
c) Out of the 100 samples provided by the manufacturer, at most how many can be defective for you to agree to use the new product?
The engineer agrees to use the new product when less than 8% of the products we subsequently purchase will be defective.
8% of the product = 0.08 × 100 = 8.
Meaning that the engineer agrees to subsequently purchase the product if less than 8 out of 100 are defective.
So, the maximum number of defective product in the sample that will still let the engineer purchase the products will be 7.
(d) For better or worse, your boss convinces you to go through with the deal. Turns out the minimum order is 5000 pieces. Assuming you purchase that many pieces of the new product, and that you found 6 defective pieces out of the 100, generate a 90% two-sided confidence interval for the number of pieces that will be flawed.
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = 0.495
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 90% confidence interval for sample size of 100 using the t-tables since information on the population standard deviation.
Degree of freedom = n - 1 = 100 - 1 = 99
Significance level = (100-90)/2 = 5% = 0.05
Critical value = t(0.05, 99) = 1.660
Standard error of the mean = σₓ = √[p(1-p)/n]
p = 0.06
n = sample size = 100
σₓ = (0.06/√100) = 0.006
σₓ = √[0.06(0.94)/100] = 0.0237486842 = 0.02375
90% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.06 ± (1.660 × 0.02375)
CI = 0.06 ± 0.039425
90% CI = (0.020575, 0.099425)
90% Confidence interval = (0.0206, 0.0994)
If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be
5000 × (0.0206, 0.0994) = (103, 497)
Hope this Helps!!!
(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less (b) A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it (c) at most 12 defective products can be found in the sample for the deal to proceed. (d) the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.
(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less. The alternative hypothesis [tex]\(H_1\)[/tex] is that the proportion of defective products is greater than 8%. Mathematically, this can be expressed as:
[tex]\(H_0: p \leq 0.08\) \(H_1: p > 0.08\)[/tex]
(b) A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it, concluding that the proportion of defective products is greater than 8%. This would mean unnecessarily turning down a good deal and potentially incurring additional costs to find another supplier.
(c) To ensure a 90% confidence level with a maximum defective rate of 8%, we can use the binomial distribution to find the maximum number of defective products allowed in the sample of 100. The formula for a binomial confidence interval is given by:
[tex]\(n \cdot p \pm Z_{\alpha/2} \sqrt{n \cdot p \cdot (1 - p)}\)[/tex]
where [tex]\(n\)[/tex] is the sample size, [tex]\(p\)[/tex] is the defect rate, and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score corresponding to the desired confidence level. For a 90% confidence level, [tex]\(Z_{\alpha/2} = 1.645\)[/tex]. Plugging in the values:
[tex]\(100 \cdot 0.08 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot (1 - 0.08)}\)[/tex]
[tex]\(8 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot 0.92}\)[/tex]
[tex]\(8 \pm 1.645 \sqrt{7.36}\)[/tex]
[tex]\(8 \pm 1.645 \cdot 2.713\)[/tex]
[tex]\(8 \pm 4.46\)[/tex]
The interval is from [tex]\(8 - 4.46\) to \(8 + 4.46\)[/tex], which gives us a range from approximately 3.54 to 12.46. Since we cannot have a fraction of a defective product, we round down to 3. Therefore, at most 12 defective products can be found in the sample for the deal to proceed.
(d) To generate a 90% two-sided confidence interval for the number of defective pieces out of 5000, given that 6 defective pieces were found out of 100, we first calculate the sample proportion of defective products:
[tex]\(\hat{p} = \frac{6}{100} = 0.06\)[/tex]
The formula for the confidence interval is:
[tex]\(\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\)[/tex]
where [tex]\(n\)[/tex] is the sample size (100 in this case), and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score for a 90% confidence level (1.645). Plugging in the values:
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06(1 - 0.06)}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06 \cdot 0.94}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.0564}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \cdot \sqrt{0.000564}\)[/tex]
[tex]\(0.06 \pm 1.645 \cdot 0.0237\)[/tex]
[tex]\(0.06 \pm 0.0391\)[/tex]
The interval is from [tex]\(0.06 - 0.0391\) to \(0.06 + 0.0391\)[/tex], which gives us a range from approximately 0.0209 to 0.0991. To find the number of defective pieces in the order of 5000, we multiply these proportions by 5000:
Lower bound: [tex]\(0.0209 \cdot 5000 = 104.5\)[/tex](round to 105)
Upper bound: [tex]\(0.0991 \cdot 5000 = 495.5\)[/tex] (round to 496)
Therefore, the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.
An angle measures 48° more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
66 and 114 degrees
Step-by-step explanation:
Supplementary angles add to 180 degrees.
An angle measures 48 more than its supplementary angle. If the supplementary angle is x, then the other angle must be x+48
x+x+48=180
Subtract 48 from both sides
x+x+48-48=180-48
x+x=132
Combine like terms
2x=132
Divide both sides by 2
2x/2=132/2
x=66
So, one of the angles is 66 degrees. The other is x+48
x+48
66+48=114
One of the angles is 66 degrees, the other is 114 degrees
Answer:
96
Step-by-step explanation:
After a college football team once again lost a game to their archrival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favored firing the coach. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To do this they test the hypotheses H0: p = 0.50 versus Ha: p > 0.50.
(A) What is the P-value for this hypothesis test?
The P-value for this hypothesis test is 0.0228.
Explanation:To find the P-value for this hypothesis test, we need to calculate the proportion of alumni who favored firing the coach in the sample. Out of 100 alumni, 64 were in favor. So, the sample proportion is 64/100 = 0.64.
Now, we need to calculate the test statistic, which follows a normal distribution. The formula for the test statistic is: z = (p' - p) / sqrt(p * (1-p) / n), where p' is the sample proportion, p is the claimed proportion under the null hypothesis, and n is the sample size.
Plugging in the values, we get: z = (0.64 - 0.50) / sqrt(0.50 * (1-0.50) / 100) = 2.00
The P-value is the probability of observing a test statistic as extreme as 2.00, assuming the null hypothesis is true. We can look up this probability in a standard normal distribution table or use a statistical software. In this case, the P-value is 0.0228.
An aerosol can contains gases under a pressure
of 4.5 atm at 24 ◦C. If the can is left on a
hot sandy beach, the pressure of the gases
increases to 4.66 atm. What is the Celsius
temperature on the beach?
Answer:
temperature on the beach = T2 = 34.56 °C
Step-by-step explanation:
We are given;
P1 = 4.5 atm
T1 = 24 °C = 24 + 273 = 297 K
P2 = 4.66 atm
Thus, P1/T1 = P2 /T2
So, T2 = P2•T1/P1
Thus, T2 = (4.66x 297)/4.5
T2 = 307.56 K
Let's convert to °C to obtain ;
T2 = 307.56 - 273
T2 = 34.56 °C
There is 60 minutes in a day. How many minutes in 24 hour day
Answer:
there is 60 minutes in a day or in a hour?
according to 60 min in a hour
Answer: 24*60= 1440 min
Step-by-step explanation:
its impossible to have 60 min in a day.
There are 1440 minutes in a 24 hour day. You can find this by multiplying the number of hours (24) by the number of minutes in an hour (60).
Explanation:The subject of your question is related to the conversion of units of time. In this case, you want to convert hours into minutes. We know that one hour is equivalent to 60 minutes. Hence, if we want to find out how many minutes are there in a 24 hour day, we will multiply the number of hours (24) by the conversion factor, which is 60 minutes per hour.
So, 24 hours * 60 minutes/hour = 1440 minutes. Therefore, there are 1440 minutes in a 24 hour day. It's straightforward when you use correct conversion factor properly.
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Taylor and Jesse are buying a magazine for $3.75 and a snack for $2.49 what is s the total cost of the two items?
Hey There!
The answer you are looking for is; $6.24!
Work:
You simply add $3.75 + $2.49 together.
Since .75 + .29 = 1.24, you carry the one over to the full dollar.
3 + 2 + 1 = 6.
= 6.24
Hope I helped! 5 stars and brainliest are always appreciated.
Answer:
6.24
Step-by-step explanation:
you add the two numbers
Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction. Price in Dollars 26 29 32 38 47 Number of Bids 12 13 15 16 18 Step 3 of 3 : Calculate the correlation coefficient, r. Round your answer to three decimal places.\
Answer:
Let's assume the following data:
Price in Dollars (X) 26 29 32 38 47
Number of Bids (Y) 12 13 15 16 18
For our case we have this:
n=10 [tex] \sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118[/tex]
[tex]r=\frac{5(2623)-(172)(74)}{\sqrt{[5(6194) -(172)^2][5(1118) -(74)^2]}}=0.974[/tex]
So then the correlation coefficient would be r =0.974
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
Solution to the problem
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
Let's assume the following data
Price in Dollars (X) 26 29 32 38 47
Number of Bids (Y) 12 13 15 16 18
For our case we have this:
n=10 [tex] \sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118[/tex]
[tex]r=\frac{5(2623)-(172)(74)}{\sqrt{[5(6194) -(172)^2][5(1118) -(74)^2]}}=0.974[/tex]
So then the correlation coefficient would be r =0.974
The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 1000 voters in the town and found that 54% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 50%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
[tex]z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=2.530[/tex]
[tex]p_v =P(z>2.530)=0.0057[/tex]
Step-by-step explanation:
Data given and notation
n=1000 represent the random sample taken
[tex]\hat p=0.54[/tex] estimated proportion of residents that favored the annexation
[tex]p_o=0.5[/tex] is the value that we want to test
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5:
Null hypothesis:[tex]p \leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info required we can replace in formula (1) like this:
[tex]z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=2.530[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>2.530)=0.0057[/tex]
Harper works as a carpenter for $20.87/h. How much will he earn in a 40-hour workweek? *
Answer:
$834.8 dollars that week
Step-by-step explanation:
All you have to do is multiply $20.87 by 10 hours to get your answer:)
By multiplying Harper's hourly wage ($20.87) by 40 hours, we determined that Harper will earn $834.80 in a 40-hour workweek.
Explanation:To calculate how much Harper will earn in a 40-hour work week, you simply need to multiply his hourly wage by the number of hours he works. In this case, that's $20.87 times 40. Using direct multiplication:
$20.87 x 40 = $834.80
So, Harper will earn $834.80 in a 40-hour workweek.
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In a random sample of n1 = 156 male Statistics students, there are x1 = 81 underclassmen. In a random sample of n2 = 320 female Statistics students, there are x2 = 221 underclassmen. The researcher would like to test the hypothesis that the percent of males who are underclassmen stats students is less than the percent of females who are underclassmen stats students. What is the p-value for the test of hypothesis? i.e. Find P(Z < test statistic). Enter your answer to 4 decimal places.
Answer:
The p-value for the test of hypothesis is P(z<-3.617)=0.0002.
Step-by-step explanation:
Hypothesis test on the difference between proportions.
The claim is that the percent of males who are underclassmen stats students (π1) is less than the percent of females who are underclassmen stats students (π2).
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2<0[/tex]
The male sample has a size n1=156. The sample proportion is p1=81/156=0.52.
The female sample has a size n2=221. The sample proportion in this case is p2=221/320=0.69.
The weigthed average of proportions p, needed to calculate the standard error, is:
[tex]p=\dfrac{n_1p_1+n_2p_2}{n_1+n_2}=\dfrac{81+221}{156+320}=\dfrac{302}{476}= 0.63[/tex]
The standard error for the difference in proportions is:
[tex]\sigma_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.63*0.37}{156}+\dfrac{0.63*0.37}{320}}\\\\\\\sigma_{p1-p2}=\sqrt{\dfrac{0.2331}{156}+\dfrac{0.2331}{320}}=\sqrt{0.001503871+0.000728438}=\sqrt{0.002232308}\\\\\\\sigma_{p1-p2}=0.047[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_1-p_2}{\sigma_{p1-p2}}=\dfrac{0.52-0.69}{0.047}=\dfrac{-0.17}{0.047}=-3.617[/tex]
The P-value for this left tailed test is:
[tex]P-value = P(z<-3.617)=0.00015[/tex]
Answer:
[tex]z=\frac{0.519-0.691}{\sqrt{0.634(1-0.634)(\frac{1}{156}+\frac{1}{320})}}=-3.657[/tex]
[tex]p_v =P(Z<-3.657)=0.0001[/tex]
Step-by-step explanation:
Data given and notation
[tex]X_{1}=81[/tex] represent the number of males underclassmen
[tex]X_{2}=221[/tex] represent the number of females underclassmen
[tex]n_{1}=156[/tex] sample of male
[tex]n_{2}=320[/tex] sample of female
[tex]p_{1}=\frac{81}{156}=0.519[/tex] represent the proportion of males underclassmen
[tex]p_{2}=\frac{221}{320}= 0.691[/tex] represent the proportion of females underclassmen
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the value for the test (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the percent of males who are underclassmen stats students is less than the percent of females who are underclassmen stats students , the system of hypothesis would be:
Null hypothesis:[tex]p_{1} \geq p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} < p_{2}[/tex]
We need to apply a z test to compare proportions, and the statistic is given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{81+221}{156+320}=0.634[/tex]
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
[tex]z=\frac{0.519-0.691}{\sqrt{0.634(1-0.634)(\frac{1}{156}+\frac{1}{320})}}=-3.657[/tex]
Statistical decision
For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test.
Since is a one side test the p value would be:
[tex]p_v =P(Z<-3.657)=0.0001[/tex]
Which function does a criminologist perform?
Answer:
To find why the crimes were committed
Jay had $80. He spent 2/5 to buy new running shows. How much did Jay spend?
Answer:
32$
Step-by-step explanation:
first divide 80 by 5.
(you should get 16)
next multiply by 2
(you should get 32)
this works because out of the 80$ he spent 2/5 of his money. you basically are multiplying the numerators and then dividing by the denominators and because 80 is a whole number it works without having to use the 1.
another way to do it is multiply 80/1 by 2/5
you should get 160/5 and when you simplify you should get 32
Jay spent $32 on new running shoes, which is calculated by taking 2/5 of his original $80.
The solution can be solved as: Jay had $80 and spent 2/5 of his money on new running shoes. To find out how much Jay spent, we need to calculate 2/5 of $80.
First, we divide $80 by 5 to find out how much 1/5 of his money is:
1/5 of $80 = $80 / 5 = $16
Now, we multiply this amount by 2 to get 2/5:
2/5 of $80 = 2 x $16 = $32
So, Jay spent $32 on new running shoes.
Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that none of the four cans selected contains an incorrect mix of paint.
Answer:
The probability that none of the four cans selected contains an incorrect mix of paint is P=0.2545.
Step-by-step explanation:
We have 12 cans, out of which 3 are defective (incorrect mix of paint).
The man will choose 4 cans to paint his mother's house living room.
Let x = the number of the paint cans selected that are defective.
The variable x is known to follow a hypergeometric distribution.
The probability of getting k=0 defectives in a selected sample of K=4 cans, where there are n=3 defectives in the population of N=12 cans is:
[tex]P(X=k)=\dfrac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}\\\\\\\\ P(X=0)=\dfrac{\binom{4}{0}\binom{12-4}{3-0}}{\binom{12}{3}}=\dfrac{\binom{4}{0}\binom{8}{3}}{\binom{12}{3}}=\dfrfac{1*56}{220}=\dfrac{56}{220}=0.2545[/tex]
The probability that none of the four cans selected contains an incorrect mix of paint is P=0.2545.
Final answer:
The probability that none of the four randomly selected cans are defective is approximately 0.2545, or 25.45%, which is determined using the hypergeometric distribution.
Explanation:
The student is faced with a scenario where a man has twelve 1-gallon paint cans, out of which three contain an incorrect mix of paint. The man randomly selects four of these cans to paint with, and the question is to find the probability that none of the four selected cans are defective, which follows the hypergeometric distribution.
The relevant parameters for the hypergeometric distribution in this scenario are: the total number of cans (N=12), the number of defective cans (K=3), the number of cans selected (n=4), and the number of defective cans selected that we are interested in (x=0). To compute the probability, we use the hypergeometric probability formula:
P(X = x) = [(C(K, x) * C(N-K, n-x)) / C(N, n)]
Substituting the given values, we have:
P(X = 0) = [(C(3, 0) * C(12-3, 4-0)) / C(12, 4)]
= [(1 * C(9, 4)) / C(12, 4)]
= (1 * 126) / 495
≈ 0.2545
This means the probability that none of the four randomly selected cans are defective is approximately 0.2545, or 25.45%.
Martin is playing a game . The probability of winning is 0.3 what is the probability of not winning
Answer:
0.7
Step-by-step explanation:
0.3+0.7=1.0=100%
Final answer:
The probability of not winning the game that Martin is playing is 0.7 or 70%, which is obtained by subtracting the probability of winning (0.3) from 1.
Explanation:
If Martin is playing a game where the probability of winning is 0.3, then the probability of not winning can be calculated by subtracting the probability of winning from 1. This is because the sum of the probabilities of all possible outcomes must equal 1. Since the probability of winning is 0.3, we calculate the probability of not winning as follows:
Probability of not winning = 1 - Probability of winningProbability of not winning = 1 - 0.3Probability of not winning = 0.7Therefore, the probability of not winning is 0.7 or 70%.
Hotel cost 60 per night flight cost 150 has a budget of 500 how many nights can she afford
Answer:
3 nights
Step-by-step explanation:
because 1 flight there and one flight back =300 then add 3 nights =480
Answer:
5 nights or less
Step-by-step explanation:
You can do this by writing an inequality and solving it.
Let n = number of nights.
1 hotel night costs $60. n number of hotel nights cost 60n.
The flight costs $150.
The total cost is the price of the hotel plus the price of the flight.
60n + 150
The total price must be less than or equal to $500.
[tex] 60n + 150 \le 500 [/tex]
Now we solve the inequality.
Subtract 150 from both sides.
[tex] 60n \le 350 [/tex]
Divide both sides by 60.
[tex] n \le \dfrac{350}{60} [/tex]
350 divided by 60 is 5.8333...
[tex] n \le 5.8 [/tex]
The number of night is less than or equal to 5.8, and it must be a whole number, so the most number of nights she can afford is 5.
geometry::: please help me ASAP
Answer:
102
Step-by-step explanation:
A research program used a representative random sample of men and women to gauge the size of the personal network of older adults. Each adult in the sample was asked to "please name the people you have frequent contact with and who are also important to you." The responses of 2824 adults in this sample yielded statistics on network size, that is, the mean number of people named per person was x=14.6, with a standard deviation of s=10.3 . Complete parts a through d.a- Give a point estimate for μ.b- Give an interval estimate for μ. Use a confidence coefficient of 0.95c- Comment on the validity of the followingstatement: "95% of the time, the true mean number of people named per person will fall in the interval computed in part b."Choose the correct answer below.A. The statement is correct. 95% of the time, the true mean number of people named per person will fall within an interval computed with a confidence coefficient of 0.95.B. The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b."C. The statement is incorrect. A correct statement would be"95% of the time, the true mean number of people named per person will fall outside the interval computed in part b.D. The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall outside the interval computed in part b.d- It is unlikely that the personal network sizes of adults are normally distributed. In fact, it is likely that the distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidenceinterval?A. It does impact the validity of the interpretation because the interpretation is based on highly skewed resultsB. It does impact the validity of the interpretation because the interpretation was based upon a sample instead of the entire population.C. It does not impact the validity of the interpretation because the interpretation is based on highly skewed results.D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.
Answer:
a. [tex]\mu=\bar x =14.6[/tex]
b. The 95% CI for the population mean is (14.22, 14.98).
c. B. "The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b"
d. D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.
Step-by-step explanation:
a) The sample mean provides a point estimation of the population mean.
In this case, the estimation of the mean is:
[tex]\mu=\bar x =14.6[/tex]
b) With the information of the sample we can estimate the
As the sample size n=2824 is big enough, we can aproximate the t-statistic with a z-statistic.
For a 95% CI, the z-value is z=1.96.
The sample standard deviation is s=10.3.
The margin of error of the confidence is then calculated as:
[tex]E=z\cdot s/\sqrt{n}=1.96*10.3/\sqrt{2824}=20.188/53.141=0.38[/tex]
The lower and upper limits of the CI are:
[tex]LL=\bar x-z\cdot s/\sqrt{n}=14.6-0.38=14.22\\\\UL=\bar x+z\cdot s/\sqrt{n}=14.6+0.38=14.98[/tex]
The 95% CI for the population mean is (14.22, 14.98).
c. "95% of the time, the true mean number of people named per person will fall in the interval computed in part b"
The right answer is:
B. "The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b"
The confidence interval gives bounds within there is certain degree of confidence that the true population mean will fall within.
It does not infer nothing about the sample means or the sampling distribution. It only takes information from a sample to estimate a interval for the population mean with certain degree of confidence.
d. It is unlikely that the personal network sizes of adults are normally distributed. In fact, it is likely that the distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidence interval?
The answer is:
D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.
The reliability of a confidence interval depends more on the sample size, not on the distribution of the population. As the sample size increases, the absolute value of the skewness and kurtosis of the sampling distribution decreases. This sample size relationship is expressed in the central limit theorem.
The point estimate for μ is 14.6. The confidence interval will provide the range where the true mean falls with 95% confidence. The Central Limit Theorem suggests that the deviation from the normal distribution will not significantly affect the answers.
Explanation:a- The point estimate for μ is x=14.6. This is calculated as the mean of all measured values.
b- An interval estimate can be calculated with the formula: x ± Z*(s/√n) where Z is the Z-value from a Z-table corresponding to desired confidence level, here, 0.95. The result would give you the range in which the true mean, μ, falls with 95% confidence.
c- The correct answer is B: The statement is incorrect. A correct statement would be "One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b."
d- If the personal network sizes of adults are not normally distributed and the distribution is highly skewed, it will have an impact on the validity of inferences derived from the confidence interval. The correct answer is D: It does not impact the validity of the interpretation as the sampling space of the sample mean will still be approximately normal due to the Central Limit Theorem.
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An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 29 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and 0.35, respectively. Is there enough evidence to reject the company’s claim at the α = 0.05 level of significance?
The question asks to perform a hypothesis test about the mean pH level in a river. Given a sample size of 29, a sample mean of 6.7, a sample standard deviation of 0.35, and a significance level of α = 0.05, the provided reference suggests that there is insufficient evidence to reject the company's claim of a mean pH of 6.8, due to the calculated p-value being greater than α.
Explanation:In this problem, we are testing the hypothesis that the mean pH level of water in a nearby river is 6.8. The company claims this as the true population mean. The hypothesis under test is called the Null hypothesis.
Null Hypothesis H0: µ = 6.8Alternative Hypothesis HA: µ ≠ 6.8The level of significance is given as α = 0.05. We have a sample of size 29 with mean 6.7 and standard deviation 0.35.
In hypothesis testing, we calculate a test statistic and compare it with a critical value corresponding to the level of significance α. Here, we would be calculating a t-score because we have the sample standard deviation, not the population standard deviation and the sample size is less than 30. If the test statistic falls in the critical region, then we reject the null hypothesis.
Without specific calculations, the given reference suggests that the decision is to not reject the null hypothesis, citing p-value > α. In this case, the calculated p-value from testing statistics is higher than 0.05, meaning that the observed test statistic would be quite likely if the null hypothesis is true.
This results in the conclusion that there is insufficient evidence in the sampled data to reject the company's claim of a mean pH of 6.8.
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There is not enough evidence to reject the company's claim at the α=0.05 level of significance.
Given:
Population mean =6.8
Sample mean =6.7
Sample standard deviation s=0.35
Sample size n=29
Level of significance α=0.05
We'll perform a one-sample t-test since the population standard deviation is unknown and the sample size is less than 30.
The hypotheses are:
Null hypothesis (o):
The mean pH level of the water in the river is 6.8 (μ=6.8).
Alternative hypothesis (H1):
The mean pH level of the water in the river is not equal to 6.8 (≠6.8)
We'll use the formula for the test statistic of a one-sample t-test:
t = (x- ) / [tex]\frac{s}{\sqrt{n} }[/tex]
t= -0.1/ 0.0651
t≈−1.535
Now, we'll find the critical value for a two-tailed test at α=0.05 significance level with n−1=28 degrees of freedom. Using a t-distribution table or statistical software,
we find the critical values to be approximately ±2.048.
Since −1.535 falls within the range −2.048 to 2.048, we fail to reject the null hypothesis.
So, there is not enough evidence to reject the company's claim at the α=0.05 level of significance.
Decompose fraction 2 3/4
To decompose the fraction 2 3/4, convert it to an improper fraction by multiplying the whole number by the denominator of the fraction, add the numerator, and place over original denominator, resulting in 11/4.
Explanation:The question asks to decompose the fraction 2 3/4 into its components. To decompose this mixed number, we need to convert it to an improper fraction. The process involves multiplying the whole number by the denominator of the fraction part, adding the numerator of the fraction part, and then placing the result over the original denominator.
Therefore, the mixed number 2 3/4 decomposed into an improper fraction is 11/4.
To avoid a service fee, your checking account balance must be at least $300 at the end of each month. Your current balance is $337.03. You use your debit card to spend $132.78. What possible amounts can you deposit into your account by the end of the month to avoid paying the service fee?
A deposit of at least $95.75 is needed to avoid the service fee, as this will bring the balance from $204.25 back to the required $300 minimum.
To avoid a service fee, we need to ensure that the checking account balance is at least $300 at the end of the month. Starting with a balance of $337.03 and after spending $132.78, the new balance is calculated as follows:
$337.03 - $132.78 = $204.25.
To avoid the service fee, the account balance must return to at least $300. Therefore, you need to deposit the difference between your current balance and the minimum balance required:
$300 - $204.25 = $95.75.
Any deposit amount greater than or equal to $95.75 will therefore avoid the service fee.
EXAMPLE 2 Prove that 9ex is equal to the sum of its Maclaurin series. SOLUTION If f(x) = 9ex, then f (n + 1)(x) = for all n. If d is any positive number and |x| ≤ d, then |f (n + 1)(x)| = ≤ 9ed. So Taylor's Inequality, with a = 0 and M = 9ed, says that |Rn(x)| ≤ (n + 1)! |x|n + 1 for |x| ≤ d. Notice that the same constant M = 9ed works for every value of n. But, from this equation, we have lim n → [infinity] 9ed (n + 1)! |x|n + 1 = 9ed lim n → [infinity] |x|n + 1 (n + 1)! = . It follows from the Squeeze Theorem that lim n → [infinity] |Rn(x)| = 0 and therefore lim n → [infinity] Rn(x) = for all values of x. By this theorem, 9ex is equal to the sum of its Maclaurin series, that is, 9ex = [infinity] 9xn n! n = 0 for all x.
Answer:
To Prove: [tex]9e^x[/tex] is equal to the sum of its Maclaurin series.
Step-by-step explanation:
If [tex]f(x) = 9e^x[/tex], then [tex]f ^{(n + 1)(x)} =9e^x[/tex] for all n. If d is any positive number and |x| ≤ d, then [tex]|f^{(n + 1)(x)}| = 9e^x\leq 9e^d.[/tex]
So Taylor's Inequality, with a = 0 and M = [tex]9e^d[/tex], says that [tex]|R_n(x)| \leq \dfrac{9e^d}{(n+1)!} |x|^{n + 1} \:for\: |x| \leq d.[/tex]
Notice that the same constant [tex]M = 9e^d[/tex] works for every value of n.
But, since [tex]lim_{n\to\infty}\dfrac{x^n}{n!} =0 $ for every real number x$[/tex],
We have [tex]lim_{n\to\infty} \dfrac{9e^d}{(n+1)!} |x|^{n + 1} =9e^d lim_{n\to\infty} \dfrac{|x|^{n + 1}}{(n+1)!} =0[/tex]
It follows from the Squeeze Theorem that [tex]lim_{n\to\infty} |R_n(x)|=0[/tex] and therefore [tex]lim_{n\to\infty} R_n(x)=0[/tex] for all values of x.
[tex]THEOREM\\If f(x)=T_n(x)+R_n(x), $where $T_n $is the nth degree Taylor Polynomial of f at a and $ lim_{n\to\infty} R_n(x)=0 \: for \: |x-a|<R, $then f is equal to the sum of its Taylor series on $ |x-a|<R[/tex]
By this theorem above, [tex]9e^x[/tex] is equal to the sum of its Maclaurin series, that is,
[tex]9e^x=\sum_{n=0}^{\infty}\frac{9x^n}{n!}[/tex] for all x.
What does the confidence interval tell about the population of all adult females? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. We are 90% confident that the interval from nothing to nothing actually contains the true mean attractiveness rating of all adult females. (Round to one decimal place as needed.) B. We are confident that 90% of all adult females have attractiveness ratings between nothing and nothing. (Round to one decimal place as needed.) C. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females.
Answer:
A. We are 90% confident that the interval from nothing to nothing actually contains true mean attractiveness rating of all adult females.
Step-by-step explanation:
The population is set of items which are similar in nature and that are to be observed for an outcome. The Confidence Interval is a defined probability that the parameters lies in this range. Population parameter is quantity which enters in probability distribution of random variable. In the given question the confidence interval is 90% which means the parameters lies within this range.
5(y+4)=6y need help in this math is for my son
Answer:
y =20
Step-by-step explanation:
5(y+4)=6y
Distribute
5y +20 = 6y
Subtract 5y from each side
5y-5y+20=6y-5y
20 =y
Answer:
solution
5y+20=6y
5y-6y=20
-y=20
Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is that housing prices follow an approximately normal model with mean $238,000 and standard deviation $5,041.
(a) What proportion of housing prices in Athens are less than $234,000? (3 decimal places)
(b) A realtor takes a random sample of 134 houses in Athens. Determine the probability the average selling price is greater than $239,000? (3 decimal places)
(c) A realtor in Asheville, NC wants to estimate the mean housing price of houses in Asheville. The realtor believes the distribution of housing prices in Asheville is similar to those in Athens.
If this realtor takes a random sample of 134 homes in Asheville, what is the standard error of the estimate? (3 decimal places)
How many homes in Asheville should the realtor sample to be 98% confident the estimate is within $500 of the true mean price? Use the critical value to exactly 3 decimal places.
Answer:
a) 0.214 or 21.4%
b) P=0.011
c) The realtor should sample at least 551 homes.
Step-by-step explanation:
The current thinking is that housing prices follow an approximately normal model with mean $238,000 and standard deviation $5,041.
a) We need to know the proportion of housing prices in Athens that are less than $234,000. We can calculate this from the z-score for the population distribution.
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{234,000-238,000}{5,041}=\dfrac{-4,000}{5.041}=-0.793\\\\\\ P(x<234,000)=P(z<-0.793)=0.214[/tex]
The proportion of housing prices in Athens that are less than $234,000 is 0.214.
b) Now, a sample is taken. The size of the sample is n=134.
We have to calculate the probability that the average selling price is greater than $239,000.
In this case, we have to use the standard error of the sampling distribution to calculate the z-score:
[tex]z=\dfrac{\bar x-\mu}{\sigma/\sqrt{n}}=\dfrac{239,000-238,000}{5,041/\sqrt{134}}=\dfrac{1,000}{435.476}= 2.296 \\\\\\P(\bar x>239,000)=P(z>2.296)=0.011[/tex]
The probability that the average selling price is greater than $239,000 is 0.011.
c) We have another sample taken from a distribution with the same parameters.
We have to calculate the sample size so that the margin of error for a 98% confidence interval is $500.
The expression for the margin of error of the confidence interval is:
[tex]E=z\cdot \sigma/\sqrt{n}[/tex]
We can isolate n from the margin of error equation as:
[tex]E=z\cdot \sigma/\sqrt{n}\\\\\sqrt{n}=\dfrac{z\cdot \sigma}{E}\\\\n=(\dfrac{z\cdot \sigma}{E})^2[/tex]
We have to look for the critical value of z for a 98% CI. This value is z=2.327.
Now we can calculate the minimum value for n to achieve the desired precision for the interval:
[tex]n=(\dfrac{z\cdot \sigma}{E})^2\\\\\\n=(\dfrac{2.327*5,041}{500})^2= 23.461 ^2=550.410\approx551[/tex]
The realtor should sample at least 551 homes.
Answer:
a) 0.214 or 21.4%
b) P=0.011
c) The realtor should sample at least 551 homes
Step-by-step explanation:
An ant moves along the x-axis from left to right at 5 inches per second. A spider moves along the y-axis from up to down at 3 inches per second. At a certain instant, the ant is 4 inches to the right of the origin and the spider is 8 inches above the origin. At this instant, what is the rate of change of the distance between the spider and the ant
Answer: The rate of change of the distance between the spider and the ant is 4.92 inches/sec
Step-by-step explanation: Please see the attachments below
Find BC if BC=x+2, AB=2x-6, and AC=17.
Answer:
BC = 9
Step-by-step explanation:
Assuming this is a straight line
AB + BC = AC
2x-6 + x+2 = 17
Combine like terms
3x -4 = 17
Add 4 to each side
3x-4+4 = 17+4
3x = 21
Divide each side by 3
3x/3 =21/3
x =7
We want to find BC
BC =x+2
=7+2
=9
what is the area of the base.(area=6 square in.x 5 in.
Answer:
30 square inch
Step-by-step explanation:
[tex]area \: of \: base = 6 \times 5 = 30 \: {inch}^{2} \\ [/tex]
A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10. The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
To find the minimum score needed to receive a grade of A, we need to determine the cutoff point for the top 16.6% of students. We can use the Z-score formula to convert a raw score into a standardized score and then find the corresponding raw score. The minimum score needed to receive a grade of A is approximately 88.
Explanation:To find the minimum score needed to receive a grade of A, we need to determine the cutoff point for the top 16.6% of students. In a normal distribution, we can use the Z-score formula to convert a raw score into a standardized score. We need to find the Z-score that corresponds to the 83.4th percentile, as 16.6 percent is the area to the left of this score. We can then use the Z-score formula to find the corresponding raw score.
Z = (X - μ) / σ
Where: Z is the Z-score, X is the raw score, μ is the mean, and σ is the standard deviation. Rearranging the formula, we have:
X = (Z * σ) + μ
Since the mean is 78 and the standard deviation is 10, we substitute the values into the formula:
X = (Z * 10) + 78
Next, we need to find the Z-score that corresponds to the 83.4th percentile using a Z-score table or a calculator. From the table, we find that the Z-score is approximately 0.9998. Substituting this value into the formula, we can solve for X:
X = (0.9998 * 10) + 78
X = 9.998 + 78
X ≈ 87.998
Therefore, the minimum score needed to receive a grade of A is approximately 88.
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Brooklyn bought 1 pound of cucumbers for a salad. She bought twice as much lettuce. How many ounces of lettuce did Brooklyn buy for the salad.
Answer:
32 ounces
Step-by-step explanation:
She bought 1 cucumber. She bought twice as much lettuce.
1(2) = 2 lbs of lettuce.
There are 16 ounces to the lb.
2 (16 ounces) = 32 ounces
Answer:
She bought 32 oz of lettuce.
Step-by-step explanation:
There are 16 oz in 1 lb. twice as much means 2x. 2 x 16 = 32.
A survey of data base administrators is conducted. In a random sample of equation, n=150, x=63 of them were found to have over 10 years of experience. Construct 1-a=0.90 confidence interval for the population proportion p of data base administrators with over 10 years of experience.____________________________________________________________1) The sample proportion of data base administrators having over 10 years of experiences is closest toa.63 b.1.645 c.4.2 d.42 e.none of the above2) The half width of this confidence interval is closest to a.0.0033 b.0.0403 c.0.0663 d.0.0790 e.none of the above3) The left limit of this confidence interval L is closest to a.0.4990 b.0.4863 c.0.3537 d.0.3140 e.none of the above4) The right limit of this confidence interval R is closest to a.0.4990 b.0.4863 c.0.3537 d.0.3410 e.none of the above5) The conclusion is a.With 90% confidence, 0.3410 < p < 0.4863 b.With 90% confidence, 0.3537 < p < 0.4990 c.With 90% confidence, 0.3410 < p < 0.4990 d.With 90% confidence, 0.3537 < p < 0.4863 e.none of the above
Answer:
Step-by-step explanation:
Sample proportion is x/n
Where
p = probability of success
n = number of samples
p = x/n = 63/150 = 0.42
q = 1 - p = 1 - 0.42 = 0.58
To determine the z score, we subtract the confidence level from 100% to get α
Since 1 - α = 0.9
α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645
Confidence interval is written as
(Sample proportion ± margin of error)
Margin of error = z × √pq/n
= 1.645 × √(0.42 × 0.58)/150
= 0.066
The lower end of the confidence interval is
0.42 - 0.066 = 0.354
The upper end of the confidence interval is
0.42 + 0.066 = 0.486
Therefore, the answers to the given questions are
1) d. 0.42
2) the quantity after the ± is the half width. It is also the margin of error. Thus
The half width of this confidence interval is closest to
d. 0.0663
3) c.0.3537
4) b.0.4863
5) d.With 90% confidence, 0.3537 < p < 0.4863
Over the past year, the vice president for human resources at a large medical center has run a series of three-month workshops aimed at increasing worker motivation and performance. To check the effectiveness of the workshops, she selected a random sample of 35 employees from the personnel files and recorded their most recent annual performance ratings, along with their ratings prior to attending the workshops. If the vice president for human resources wishes to assess the effectiveness of the workshop in improving performance ratings, what sort of test should she use?
Answer: She should use THE PAIRED SAMPLE T-TEST.
Step-by-step explanation: The Paired sample t-test, is a method used in statistics to determine whether the mean difference in a statistics is zero. Which shows the accuracy of the two different recorded observation.
The paired sample t-test will help her to evaluate the recorded performance rating of the workers before the workshop, and after attending the workshop.
Example:
Let the mean in the workers performance rating before the workshop be Mb, and after the worship be Ma.
If she wants to find how significant the workshop was.
Ma - Mb = 0 means the workshop did not have any influence in their performance, as their performance remains the same.
Ma - Mb > 0 means that the workshop has improved the performance of the workers. As their mean performance after the workshop is greater than their mean performance before the workshop.
Ma - Mb <0 means that the workshop has reduced the performance of the workers. As their mean performance before the workshop is greater than their mean performance after the workshop.