Answer:
The type II error might have been committed because of small sample size or small significance level.
Step-by-step explanation:
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.
β = Probability of accepting H₀ when H₀ is false.
In this case we need to test the hypothesis whether the new advertising campaign increases the sales or not.
The hypothesis can be defined as:
H₀: The new advertising campaign does not increases the sales.
Hₐ: The new advertising campaign increases the sales.
The confidence level wanted here is 99%.
The type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.
The type II error could have been made because of the following reasons:
The sample size selected is too small. The smaller the sample size, greater is the probability of type II error.Significance level of the test must be small. If the significance level is small then the rejection regions decreases. Thus, reducing the chances of correctly rejecting the null hypothesis.Thus, the type II error might have been committed because of small sample size or small significance level.
ASK YOUR TEACHER An article reported that for a sample of 42 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 165.23. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)
Final answer:
To calculate a 95% confidence interval for the true average CO2 level in the population of all homes, we use the sample mean and sample standard deviation to calculate the margin of error and determine the lower and upper bounds of the confidence interval.
Explanation:
To calculate a 95% confidence interval for the true average CO2 level in the population of all homes, we can use the sample mean and sample standard deviation provided.
First, we calculate the margin of error using the formula: Margin of Error = Critical Value x (Sample Standard Deviation / sqrt(Sample Size)). The critical value for a 95% confidence interval is 1.96.
Next, we calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the sample mean respectively.
Therefore, the 95% confidence interval for the true average CO2 level in the population of all homes is (589.17, 719.15).
This means that we can be 95% confident that the true average CO2 level in the population of all homes falls within this range.
Restaurant etiquette dictates that you should leave a 18% tip for the server if the service is acceptable if that is the case how much should you tip if your total is $28.00
Answer:
$5.04
Step-by-step explanation:
A national study report indicated that 20.9% of Americans were identified as having medical bill financial issues. What if a news organization randomly sampled 400 Americans from 10 cities and found that 90 reported having such difficulty. A test was done to investigate whether the problem is more severe among these cities. What is the p-value for this test?
Answer:
The p-value for this test is 0.22065.
Step-by-step explanation:
We are given that a national study report indicated that 20.9% of Americans were identified as having medical bill financial issues.
A news organization randomly sampled 400 Americans from 10 cities and found that 90 reported having such difficulty.
Let p = proportion of Americans who were identified as having medical bill financial issues in 10 cities.
SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 20.9% {means that % of Americans who were identified as having medical bill financial issues in these 10 cities is less than or equal to 20.9%}
Alternate Hypothesis, [tex]H_A[/tex] : p > 20.9% {means that % of Americans who were identified as having medical bill financial issues in these 10 cities is more than 20.9% and is more severe}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of 400 Americans from 10 cities who were found having such difficulty = [tex]\frac{90}{400}[/tex] = 0.225 or 22.5%
n = sample of Americans = 400
So, test statistics = [tex]\frac{0.225-0.209}{{\sqrt{\frac{0.225(1-0.225)}{400} } } } }[/tex]
= 0.77
Now, P-value of the test statistics is given by the following formula;
P-value = P(Z > 0.77) = 1 - P(Z [tex]\leq[/tex] 0.77)
= 1 - 0.77935 = 0.22065
Testing the hypothesis, using the information given, it is found that the p-value is of 0.2148.
At the null hypothesis, it is tested if the proportion for these cities is of 20.9% = 0.209, hence:
[tex]H_0: p = 0.209[/tex]
At the alternative hypothesis, it is tested if the proportion for these cities is greater than 0.209, hence:
[tex]H_1: p > 0.209[/tex].
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: [tex]p = 0.209, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].
Then, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.225 - 0.209}{\sqrt{\frac{0.209(0.791)}{400}}}[/tex]
[tex]z = 0.79[/tex]
The p-value for this test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 0.79.
Looking at the z-table, z = 0.79 has a p-value of 0.7852.
1 - 0.7852 = 0.2148.
The p-value for this test is of 0.2148.
A similar problem is given at https://brainly.com/question/24166849
If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is the distance from the center to either endpoint of the diameter. Finally use the center-radius form to find the equation.
Answer:
The equation of the circle is [tex](x+3)^2+(y-5)^2 = 17[/tex]
Step-by-step explanation:
The complete question is
If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is the distance from the center to either endpoint of the diameter. Finally use the center-radius form to find the equation.
Find the center-radius form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.
Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by
[tex](\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5)[/tex].
We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by [tex]\sqrt[]{(a-c)^2+(b-d)^2}[/tex]. So, let us use (1,4) to calculate the radius.
[tex] r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}[/tex].
REcall that given a point [tex](x_0,y_0)[/tex]. The equation of a circle centered at the point [tex](x_0,y_0)[/tex] is
[tex](x-x_0)^2+(y-y_0)^2 = r^2[/tex]
In our case, [tex](x_0,y_0)=(-3,5)[/tex] and [tex] r=\sqrt[]{17}[/tex]. Then, the equation is
[tex](x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17[/tex]
According to an exit poll for an election, 55.6% of the sample size of 836 reported voting for a specific candidate. Is this enough evidence to predict who won? Test that the population proportion who voted for this candidate was 0.50 against the alternative that it differed from 0.50.
Report the test statistic and P-value and interpret the latter.
Answer:
[tex]z=\frac{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238[/tex]
[tex]p_v =2*P(z>3.238)=0.0012[/tex]
The p value is a reference value and is useful in order to take a decision for the null hypothesis is this p value is lower than a significance level given we reject the null hypothesis and otherwise we have enough evidence to fail to reject the null hypothesis.
Step-by-step explanation:
Data given and notation
n=836 represent the random sample taken
[tex]\hat p=0.556[/tex] estimated proportion of interest
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
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 ture proportion is equal to 0.5 or no.:
Null hypothesis:[tex]p=0.5[/tex]
Alternative hypothesis:[tex]p \neq 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 requires we can replace in formula (1) like this:
[tex]z=\frac{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238[/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 bilateral test the p value would be:
[tex]p_v =2*P(z>3.238)=0.0012[/tex]
The p value is a reference value and is useful in order to take a decision for the null hypothesis is this p value is lower than a significance level given we reject the null hypothesis and otherwise we have enough evidence to fail to reject the null hypothesis.
Stop&Shop is having a sale on paper towels: 5 rolls for $3. How much will 1 roll(s) cost?
Answer:
I believe it would be 0.60 cents
Step-by-step explanation:
roll 5
The cost 3
Divide the 5 by 5 to get 1 and divde 3 by 6 to get 0.60
Answer:
$0.60
Step-by-step explanation:
To work this out you would divide $3 by 5, which is 0.6. This is because we know that $3 is for 5 and so to work out 1 you would divide by 5.
1) Divide 3 by 5.
[tex]3/5=0.6[/tex]
1 roll of paper towels is $0.6.
Simplify the expression 4y^2 + 6x -2y^2 + 12x
Answer:
2y^2+18x
Step-by-step explanation:
4y^2 + 6x -2y^2 + 12x
=4y^2-2y^2+6x+12x
=2y^2+6x+12x
=2y^2+18x
Answer:
2y^2+18x
Step-by-step explanation:
4y^2+6x-2y^2+12x
=4y^2-2y^2 6x+12x
=2y^2+18x
Need answer ASAP plz and thank you
Answer:
24 cm
Step-by-step explanation:
Which of the following expressions are greater than 1? Choose all that apply.
A.
1675×5
B.
27×4
C.
33100×3
D.
1233×3
E.
1021×2
F.
319×5
Answer:
I think the answers are A, C, D, and E
Step-by-step explanation:
Estimate
137 X 18
Choose 1 answer
To estimate the product 137 multiplied by 18, we can round the numbers to the nearest ten. 137 is approximately 140, and 18 is approximately 20. The estimated product of 137 x 18 is 2800.
Explanation:To estimate the product 137 multiplied by 18, we can round the numbers to the nearest ten. 137 is approximately 140, and 18 is approximately 20. Then, we multiply the rounded numbers: 140 x 20 = 2800. Therefore, the estimated product of 137 x 18 is 2800.
Learn more about Estimating multiplication here:https://brainly.com/question/36983790
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For the next three questions use the following information to determine your answers. A research group is curious about features that can be attributed to music genres. A music streaming service provides a few different attributes for songs such as speechness, danceability, and valence. They suspect that there is a difference between the average valence (positive or negative emotion) of metal songs compared to blues songs. However, they must conduct a study to determine if that is true. From a sample of 87 metal songs, the sample mean for valence is 0.451 and the sample standard deviation is 0.139. From a sample of 94 blues songs, the sample mean for valence is 0.581 and the sample standard deviation is 0.167. Assume that sample1 comes from the sample metal songs and that sample2 comes from the sample blues songs Compute the 90% confidence interval. Please round the values to the fourth decimal point and format your response as follows: (lower_value, upper_value)
Which of the following represents the hypotheses that we will be testing, assuming that µ1 represents the population mean of valence for all metal songs and that µ2 represents the population mean of valence for all blues songs.?
a.H0: µ1 = µ2 versus Ha: µ1 > µ2
b.H0: µ1 = µ2 versus Ha: µ1 ≠ µ2
c.H0: µ1 = µ2 versus Ha: µ1 < µ2
Answer:
b
Step-by-step explanation:
Null hypothesis: mean of valence for all metal song is equal to mean of valence of blues song.
Null hypthesis tests the claim
Altenate hypothesis: mean of valence for all metal songs is not equal to mean of valence of blues song.
Alternate hypothesis rejects the claim.
Answer:
(A) Since Sample 1 comes from the population of Metal songs only and Sample 2 comes from the population of Blue songs only,
The 90% confidence interval for mean valence for Metal songs is (0.2224 , 0.6797)
The 90% confidence interval for mean valence for Blue songs is (0.3063 , 0.8557)
All intermittent and final answers were rounded up to four decimal places.
(B) The option (b) is correct. This is because the question says that the research group suspects a difference between both means, not that one mean is greater or less than the other.
Step-by-step explanation:
(A) Using a 90% confidence level, the true mean is within 1.645 standard deviations of the sample mean
For METAL SONGS,
Lower limit = 0.451 - (1.645)(0.139)
= 0.451 - 0.2287 = 0.2224
Upper limit = 0.451 + (1.645)(0.139)
= 0.451 + 0.2287 = 0.6797
For BLUE SONGS,
Lower limit = 0.581 - (1.645)(0.167)
= 0.581 - 0.2747 = 0.3063
Upper limit = 0.581 + (1.645)(0.167)
= 0.581 + 0.2747 = 0.8557
(B) The null hypothesis is:
Mean valence of Metal songs is equal to the mean valence of Blue songs
Alternative hypothesis:
Mean valence of Metal songs is NOT equal to the mean valence of Blue songs.
What is the measure of 0 in radians? In the diagram, 0 is a central angle, 3 is the radius, and pi is the arc
Given:
Given that the radius of the circle is 3 units.
The arc length is π.
The central angle is θ.
We need to determine the expression to find the measure of θ in radians.
Expression to find the measure of θ in radians:
The expression can be determined using the formula,
[tex]S=r \theta[/tex]
where S is the arc length, r is the radius and θ is the central angle in radians.
Substituting S = π and r = 3, we get;
[tex]\pi=3 \theta[/tex]
Dividing both sides of the equation by 3, we get;
[tex]\frac{\pi}{3}=\theta[/tex]
Thus, the expression to find the measure of θ in radians is [tex]\theta=\frac{\pi}{3}[/tex]
Answer:
Step-by-step explanation:
[For Questions 1 & 2]
There was once a crooked but witty man Douglas charged for the crime of
felony. He was kept in a prison cell which was guarded by a hefty officer. The
cell was situated at the beginning of a long straight corridor partitioned by five
doors. The doors operated on different time switches so that the first, which
separated the cell from the corridor, opened every 1 minute 45 seconds, the
second every 1 minute 10 seconds, the third every 2 minutes 55 seconds, the
fourth every 2 minutes 20 seconds, and the fifth, which was at the end of the
corridor, every 35 seconds. Every once in a while, the five doors opened
simultaneously. When this happened, the guard arrived, looked down the
corridor to check the cell, and then left. Douglas calculated that in making his
escape it would take 20 seconds to cover the distance between consecutive
doors, which was longer than the amount of time a door stayed open. He also
knew that if he stayed in the corridor for longer than two and a half minutes, at a
stretch, an alarm would sound. So he had to escape in the shortest possible time.
Given that Douglas was smart enough to keep the track of all time.
Question 1:How much time had already passed when Douglas started
moving?
A. 18m 40sec B. 19m 15sec C 19m 50sec D. Prisoner cannot escape
Question 2:How long before the guard returned does Douglas cleared the
last door?
12m 50sec
B 13m 25sc
D. Douglas
Answer:
B. 19 min 15 sec
B. 13 min 25 sec
Step-by-step explanation:
Door 1 opens every 1 min 45 sec, or 105 sec.
Door 2 opens every 1 min 10 sec, or 70 sec.
Door 3 opens every 2 min 55 sec, or 175 sec.
Door 4 opens every 2 min 20 sec, or 140 sec.
Door 5 opens every 35 sec.
The greatest common factor is 35 seconds, so we can measure the time in units of 35 seconds.
Door 1 opens every 3 units.
Door 2 opens every 2 units.
Door 3 opens every 5 units.
Door 4 opens every 4 units.
Door 5 opens every 1 unit.
The least common multiple of 3, 2, 5, 4, and 1, is 60. So every 60 units, all five doors will open, and the guard will look down the corridor to check on the prisoner. Douglas must escape before this time.
In order to escape in the shortest time possible, Douglas should time his escape so that each door opens 1 unit after the door before it. It takes Douglas 20 seconds to move from one door to another, so he will have enough time to get to the next door before it opens.
Let's say Douglas starts moving when Door 1 opens for the nth time. In other words, 3n units have passed before he starts moving. That means Door 2 should open after 3n + 1 units. Door 3 should open after 3n + 2 units. Door 4 should open after 3n + 3 units. And Door 5 should open after 3n + 4 units.
Since Door 2 opens every 2 units, 3n + 1 should be a multiple of 2.
Since Door 3 opens every 5 units, 3n + 2 should be a multiple of 5.
Since Door 4 opens every 4 units, 3n + 3 should be a multiple of 4.
Since Door 5 opens every 1 unit, 3n + 4 should be a multiple of 1.
By trial and error, n = 11.
So Douglas starts moving after 33 units, or 1155 seconds, or 19 min 15 sec.
Douglas clears the fifth door after 37 units, which leaves 23 units to spare, or 805 seconds, or 13 min 25 sec.
what are the steps to find the lower and upper quartiles in a data set
Answer:
The steps to finding the upper and lower quartiles are given in the first choice.
1. Order the data from least to greatest. If you don't do this, the data is random.
2. Find the median - you will do this so that you can find the midpoint of the data set (half of of the data is smaller and half of the data is larger).
3. Find the lower quartile - this is the half of the lower half of numbers; think of it as breaking the lower half of the data into 2 sections.
4. Find the upper quartile - this is the half of the greater half of numbers; this will break the upper half of the data into 2 sections.
Answer:
A.
Step-by-step explanation:
Just took the test:)
Twenty eight is 40% of
Answer:
11.20 is maybe the answer
Answer:
70
Step-by-step explanation:
Assume the unknown value is 'Y'
28 = 40% x Y
28 = 40/100 x Y
Multiplying both sides by 100 and dividing both sides of the equation by 40 we will arrive at:
Y = 3 x 100/40
Y = 70%
The labels on a shipment of the five chemicals A –E below were washed off by accident when the delivery truck went through a truckwash with the doors open. A clever student took infrared spectra of each of the resulting unknowns. Unknown #1 had a strong, broad IR absorption at 3400–3600 cm–1, and no absorptions between 1600 and 2900 cm–1. Unknown #2 had a strong absorption at 1680 cm–1 and no absorptions above 3100 cm–1. What are the structures of unknowns 1 and 2?
Answer:
Unknown 1: -OH group at 3400-3600
Unknown 2: Ketone and alkene group
Step-by-step explanation:
Unknown 1:
This compound has a strong IR absorption at 3400 - 3600cm-¹; this indicates that it is an alcoholic group (OH)
No absorption between 1600 and 2900cm-¹: this rule out the presence of ketone (C = O)
Hence the unknown compound is OH group
Unknown 2:
This has strong IR absorption at 1680cm-¹: this indicates the presence of (C=O) group.
No absorptions above 3100cm-¹: this indicates the presence of C = C - H
So therefore, unknown 2 is most likely to be Ketone and alkene group
A bag contains 20 marbles. These marbles are identical, except they are labeled with the integers 1 through 20. Five marbles are drawn at random from the bag. There are a few ways to think about this.
a. Marbles are drawn one at a time without replacement. Once a marble is drawn, it is not replaced in the bag. We consider all the lists of marbles we might create. (In this case, picking marbles 1, 2, 3, 4, 5 in that order is different from picking marbles 5, 4, 3, 2, 1.)
b. Marbles are drawn all at once without replacement. Five marbles are snatched up at once. (In this case, picking marbles 1, 2, 3, 4, 5 and picking marbles 5, 4, 3, 2, 1 are considered the same outcome.)
c. Marbles are drawn one at a time with replacement. Once a marble is drawn, it is tossed back into the bag (where it is hopelessly mixed up with the marbles still in the bag). Then the next marble is drawn, tossed back in, and so on. (In this case, picking 1, 1, 2, 3, 5 and picking 1, 2, 1, 3, 5 are different outcomes.)
Required:
For each of these interpretations, describe the sample space that models these experiments.
Answer:
a. The probability of getting an specific sequence would be
[tex](1/20)*(1/19)*(1/18)*(1/17)*(1/16)[/tex]
b. The probability of having an specific sequence would be.
[tex]5/20 = 1/4[/tex]
Step-by-step explanation:
a. If you draw 5 marbles without replacement, the probability of getting an specific sequence would be
[tex](1/20)*(1/19)*(1/18)*(1/17)*(1/16)[/tex]
b. If you draw 5 marbles all at once without replacement, the probability of having an specific sequence would be.
[tex]5/20 = 1/4[/tex]
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 80% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1. The study found that for a sample of 256 teenagers the mean number of energy drinks consumed per week is 4.7. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The 80% confidence interval for the mean
(4.6199 , 4.7801)
Step-by-step explanation:
Explanation:-
Assuming that the population standard deviation for the number of energy drinks consumed each week is 1
Given the Population standard deviation 'σ' = 1
The study found that for a sample of 256 teenagers the mean number of energy drinks consumed per week is 4.7
given sample size 'n' = 256
mean of the sample 'x⁻' = 4.7
confidence interval for the mean
The 80% confidence interval for the mean is determined by
[tex](x^{-} -Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\alpha }\frac{S.D}{\sqrt{n} } )[/tex]
the z-score of 80% level of significance = 1.282
[tex](4.7 - 1.282\frac{1}{\sqrt{256} } , 4.7 + 1.282\frac{1}{\sqrt{256} } )[/tex]
(4.7 - 0.0801 , 4.7 +0.0801)
(4.6199 , 4.7801)
Conclusion:-
The 80% confidence interval for the mean
(4.6199 , 4.7801)
margot measured the distance for 6 wavelengths of visible light as 2,400 nano meters what is the distance for 1 wavelength
Answer:
400nanometers
Step-by-step explanation:
Based on Margot measurement, the distance for 6wavelengths of visible light is 2400nanometers. To calculate the resulting distance for 1wavelength we have:
6wavelength = 2400nanometers
1wavelength = x
6wavelength × x = 2400nanometers × 1wavelength
x = 2400nanometres/6
x = 400nanometres
The titanium content in an aircraft-grade alloy is an important determinant of strength. A sample of 20 test coupons reveals the following titanium content (in percent). 8.32 8.05 8.93 8.65 8.25 8.46 8.52 8.35 8.36 8.41 8.42 8.30 8.71 8.75 8.60 8.83 8.50 8.38 8.29 8.46 Use the normal approximation for the sign test to test the claim that the median titanium content is equal to 8.5%. Use α=0.05. Calculate the observed number of plus differences. r+= Enter your answer; r+ Calculate to 2 decimal places the test statistic. z0= Enter your answer; z0 Calculate to 3 decimal places the P-value. P-value = Enter your answer; P-value H0 : μ˜=8.5 versus H1: μ˜≠8.5. Conclusion: Choose your answer; Conclusion
Answer:
attached
Step-by-step explanation:
attached
To test the claim that the median titanium content is 8.5%, we use the normal approximation for the sign test. We calculate the observed number of plus differences, the test statistic, and the P-value. We fail to reject the null hypothesis because the P-value is larger than the significance level.
Explanation:To test the claim that the median titanium content is equal to 8.5%, we can use the normal approximation for the sign test. The sign test is used when the data is not normally distributed. In this case, we have 20 test coupons with titanium content in percent. To calculate the observed number of plus differences (r+), we count the number of values greater than 8.5% and the number of values less than 8.5% in the sample. In this case, there are 7 values greater than 8.5% and 13 values less than 8.5%. Therefore, r+ = 7.
To calculate the test statistic (z0), we use the formula z0 = (r+ - n/2) / sqrt(n/4), where n is the sample size. In this case, n = 20. Plugging in the values, we get z0 = (7 - 20/2) / sqrt(20/4) = -1.5.
To calculate the P-value, we need to find the probability of observing a test statistic as extreme as -1.5 or more extreme in a standard normal distribution. We can use a statistical table or software to find the P-value. In this case, the P-value is 0.133, calculated using a standard normal distribution table.
Since the P-value (0.133) is larger than the significance level α (0.05), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the median titanium content is different from 8.5%.
6x - 2y = 12
the slope (m) of this equation is
?
*hint* you first need to put the equation in slope intercept form.
10.
Step-by-step explanation:
Here given
6x - 2y = 12
2y = 6x - 12
2y = 6(x - 2)
y = 6( x - 2)
2
y = 3(x - 2)
y = 3x - 6
Comparing with y = mx + c
so slope (m) = 3
Hope it will help you :))
A mouse walks in a maze that is an orthogonal grid made of corridors that intersect at crossings one foot apart, stopping at every intersection. Using coordinates (with units in feet), it starts at the origin, then moves equally likely up to (0, 1) or down to (0, −1) or right to (1, 0) or left to (−1, 0) by one unit until the next crossing. Then it stops, picks another random direction (up, down, right or left) equally likely and moves by another unit till the next crossing. Every time it stops, its position is a vector (a, b) where both a and b are integers. Scientists let the mouse walk n feet, after which its position is (X, Y ) and it is at distance D from the origin (D = √ X2 + Y 2).
a) What is Cov(X,Y)?
b) Are X and Y independent?
c) What is E(DP)?
Answer:
See the attached file for the answer.
Step-by-step explanation:
See the attached file for the explanation.
The mean and standard deviation of a random sample of 7 baby orca whales were calculated as 430 pounds and 26.9 pounds, respectively. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the mean weight of all baby orca whales.
a. 26.9 ± 1.895 (430/√7 )
b. 26.9 ±1.943 (430/√7)
c. 430 ±1.440 (26.9/√7)
d. 430 ± 1.895 (26.9/√7)
e. 430 ± 1.943 (26.9/√7)
Answer:
[tex]430-1.943\frac{26.9}{\sqrt{7}}[/tex]
[tex]430+1.943\frac{26.9}{\sqrt{7}}[/tex]
And the best option would be:
e. 430 ± 1.943 (26.9/√7)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=430[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=26.9 represent the sample standard deviation
n=7 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=7-1=6[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,6)".And we see that [tex]t_{\alpha/2}=1.943[/tex]
Now we have everything in order to replace into formula (1):
[tex]430-1.943\frac{26.9}{\sqrt{7}}[/tex]
[tex]430+1.943\frac{26.9}{\sqrt{7}}[/tex]
And the best option would be:
e. 430 ± 1.943 (26.9/√7)
For 90 percent confidence interval for the mean weight of all baby orca whales is,
[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]
Thus option e is the correct option.
Given-
Mean [tex]X[/tex] of the random sample is 430 pounds.
Standard deviation [tex]s[/tex] of the sample is 26.9 pounds.
Confidence interval is 90 percent.
The degree of freedom is sample size n-1. Thus,
[tex]D_f=7-1[/tex]
[tex]D_f=6[/tex]
The critical value for 90 percent confidence level is,
[tex]t_{\frac{a}{2} }=1.943[/tex]
The confidence interval of a mean can be given by,
[tex]X\pm t_{\frac{a}{2}}\dfrac{s}{\sqrt{n} }[/tex]
Put the value in above equation we get,
[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]
Taking positive sign,
[tex]430+1.943\dfrac{26.9}{\sqrt{7} }[/tex]
Taking negative sign,
[tex]430-1.943\dfrac{26.9}{\sqrt{7} }[/tex]
Hence, For 90 percent confidence interval for the mean weight of all baby orca whales is,
[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]
Thus option e is the correct option.
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Emil is purchasing a $175,000 home with a 15-year mortgage. He will make a
15% down payment. Use the table below to find his monthly PMI payment
Base-To-Loan %
Fixed-Rate Loan
30 yrs. 15 yrs.
ARM 2% + 1 Year Cap
30 yrs. 15 yrs.
95.01% to 97%
0.90%
0.79%
n/a
n/a
90.01% to 95%
0.78%
0.26%
0.92%
0.81%
85.01% to 90%
0.52%
0.23%
0.65%
0.54%
85% and Under
0.32%
0.19%
0.37%
0.26%
As per the given data in the question, Emil's monthly PMI payment is $28.81.
What is mortgage?A mortgage is a loan used to finance the purchase or upkeep of a home, land, or other types of rental properties.
The lender agrees to repay the loan over time, usually in regular installments divided into principal and interest. Loans are protected by the property.
To determine Emil's monthly PMI payment, we first need to determine the loan-to-value (LTV) ratio.
Emil is making a 15% down payment on a $175,000 home, which means his loan amount is $148,750. To calculate the LTV ratio, we divide the loan amount by the property value:
LTV ratio = loan amount / property value
LTV ratio = $148,750 / $175,000
LTV ratio = 0.85
Since Emil's LTV ratio is between 85.01% and 90%, his PMI rate for a 15-year fixed-rate loan is 0.23% according to the table.
To calculate Emil's monthly PMI payment, we multiply the loan amount by the PMI rate and divide by 12 (for the 12 months in a year):
Monthly PMI payment = (loan amount x PMI rate) / 12
Monthly PMI payment = ($148,750 x 0.23%) / 12
Monthly PMI payment = $28.81
Therefore, Emil's monthly PMI payment is $28.81.
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A recipe called for the ratio of sugar to flour to be 7 : 2. If you used 63 ounce of sugar, how many ounces
of flour would you need to use?
Answer:
18
Step-by-step explanation:
The average population growth rate for whitetail deer is 0.35. Hunting laws are set to limit the time allowed for hunting deer with a goal of achieving about a 35% mortality rate on deer to keep the population in check. Years with a higher than 35% mortality will result in an overall decline in the deer population while years with a lower than 35% mortality rate will result in an increased population. If the growth rate exceeds the mortality rate, and the net effect were a 4% growth rate, how long would it take the population of deer to double
The population of deer will double when the growth rate exceeds the mortality rate, and the net effect is a 4% growth rate. It will take approximately 17.3 years for the population to double.
Explanation:The population of deer will double when their growth rate exceeds the mortality rate and the net effect is a 4% growth rate. We can calculate the time it takes for the population to double using the formula for exponential growth:
Start with the equation for exponential growth: P = P0 * ertPlug in the values we know: 2P0 = P0 * e0.04tSolve for t by dividing both sides by P0 and taking the natural logarithm of both sides: t = ln(2) / 0.04Use a calculator to find that t is approximately 17.3 yearsLearn more about population growth rate here:https://brainly.com/question/16013460
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Determine if each of the following sets is a subspace of ℙn, for an appropriate value of n. Type "yes" or "no" for each answer.
Let W1 be the set of all polynomials of the form p(t)=at2, where a is in ℝ.
Let W2 be the set of all polynomials of the form p(t)=t2+a, where a is in ℝ.
Let W3 be the set of all polynomials of the form p(t)=at2+at, where a is in ℝ.
Answer:
1. Yes.
2. No.
3. Yes.
Step-by-step explanation:
Consider the following subsets of Pn given by
1.Let W1 be the set of all polynomials of the form [tex]p(t)=at^2[/tex], where a is in ℝ.
2.Let W2 be the set of all polynomials of the form [tex]p(t)=t^2+a[/tex], where a is in ℝ.
3. Let W3 be the set of all polynomials of the form [tex]p(t)=at^2+at[/tex], where a is in ℝ.
Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:
- The 0 vector of V is in W.
- Given v,w in W then v+w is in W.
- Given v in W and a a real number, then av is in W.
So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.
- First property:
Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.
For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.
- Second property:
W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials
[tex]p_1 (t) = at^2, p_2(t)=bt^2[/tex].
We must check that p_1+p_2(t) is in W1.
Note that
[tex]p_1(t)+p_2(t) = at^2+bt^2 = (a+b)t^2[/tex]
Since a+b is another real number, we have that p1(t)+p2(t) is in W1.
W3. Consider two elements in W3. Say [tex]p_1(t) = a(t^2+t), p_2(t)= b(t^2+t)[/tex]. Then
[tex]p_1(t) + p_2(t) = a(t^2+t) + b(t^2+t) = (a+b) (t^2+t)[/tex]
So, again, p1(t)+p2(t) is in W3.
- Third property.
W1. Consider an element in W1 [tex] p(t) = at^2[/tex]and a real scalar b. Then
[tex] bp(t) = b(at^2) = (ba)t^2)[/tex].
Since (ba) is another real scalar, we have that bp(t) is in W1.
W3. Consider an element in W3 [tex] p(t) = a(t^2+t)[/tex]and a real scalar b. Then
[tex] bp(t) = b(a(t^2+t)) = (ba)(t^2+t)[/tex].
Since (ba) is another real scalar, we have that bp(t) is in W3.
After all,
W1 and W3 are subspaces of Pn for n= 2
and W2 is not a subspace of Pn.
W1 is a subspace of ℙn, W2 is not a subspace of ℙn, and W3 is a subspace of ℙn.
Explanation:For a set to be a subspace of ℙn, it must satisfy three conditions: the zero vector must be in the set, the set must be closed under addition, and the set must be closed under scalar multiplication.
W1:To determine if W1 is a subspace of ℙn, we check if it satisfies the three conditions:
The zero vector is a polynomial of the form p(t) = 0t^2, which is in W1.If p(t) and q(t) are polynomials of the form p(t) = at^2 and q(t) = bt^2, then their sum is (a+b)t^2, which is also in W1.If p(t) is a polynomial of the form p(t) = at^2 and c is a scalar, then c * p(t) = (ca)t^2, which is in W1.Therefore, W1 is a subspace of ℙn.
W2:The zero vector is a polynomial of the form p(t) = t^2 + 0, which is in W2.If p(t) and q(t) are polynomials of the form p(t) = t^2 + a and q(t) = t^2 + b, then their sum is (t^2 + a) + (t^2 + b) = 2t^2 + (a + b), which is not in the form required by W2. Therefore, W2 is not closed under addition and is not a subspace of ℙn.W3:The zero vector is a polynomial of the form p(t) = 0t^2 + 0t, which is in W3.If p(t) and q(t) are polynomials of the form p(t) = at^2 + at and q(t) = bt^2 + bt, then their sum is (a + b)t^2 + (a + b)t, which is also in W3.If p(t) is a polynomial of the form p(t) = at^2 + at and c is a scalar, then c * p(t) = (ca)t^2 + (ca)t, which is in W3.Therefore, W3 is a subspace of ℙn.
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There is another way to rank the difficulty of test questions using Networks: Each student gives scores for each problem, then we construct a network whose nodes/vertices are the problems of the exam. There is an arc from problem A to B for student k that did better in problem B than in problem A, (i.e., if sA, sB are the scores of those problems, sB > sA). The weight of the arc yk associated to student k equals (approximately) the difference of score the student received in those two problems sB −sA = yk. Explain why the Massey’s method we saw in class can be used for rating exam problems by difficulty.
Answer:
Step-by-step explanation:
Truly, on a single student level, the Massey method can be applied i.e. problems are ranked according to their level of difficulty for a single student.
Let us say there are 4 problems P1, P2, P3, P4 set in an exam where a student has to solve any two.
Assuming student 1 solves and scores more in P1 than in P2, r1>r2
student 2 more in P1 than P4 r1>r4
student 3 more in P2 than P4 r2>r4
student 4 more in P4 than P3 r4>r3
student 5 more in P2 than P3 r2>r3
and such many more cases.
then the Massey's model can be written as
P1 P2 P3 P4
\begin{bmatrix} 1 &-1 &0 &0\\ 1 &-1 &0 &0 \\ 0 &1 & 0 &-1 \\ 0 & 0 &-1 & 1 \\ 0 & 1 & -1 & 0 \end{bmatrix}.
\times \begin{bmatrix}r1 \\r2 \\r3 \\r4 \end{bmatrix} =
\begin{bmatrix}y_{1} \\ y_{2} \\ y_{3} \\ y_{4}\\ y_{5}\end{bmatrix}.
If Pi gives more score than Pj, the entry below Pi shall be 1 and below Pj shall be -1.
The rest of the entries shall be 0.
r1,r2,r3,r4,r5 are ranks .
There may be more rows depending upon more combination of 2 problems.
Should in case more than one student solve the same combination and get scores in the same order, for instance, 12 students solve P1 and P2, for 7 of them r1>r2, then their scores can be averaged.
Normally, such systems are overdetermined, i.e., more rows than the number of unknowns, then it is solved by the Least square method ., as there shall be no a solution with least error is found out.
The overall ranking, in reverse order, shall give the ranking according to increasing difficulty.
The security department of a factory wants to know whether the true average time required by the night guard to walk his round is 30 minutes. If, in a random sample of 32 rounds, the night guard averaged 30.8 minutes with a standard deviation of 1.5 minutes, determine whether this is sufficient evidence to reject the null hypothesis µ = 30 minutes in favor of the alternative hypothesis µ 6= 30 minutes, at the 0.01 level of significance. Conduct the test using the p-value approach. Provide detailed solutions in the four steps to hypothesis testing and state your conclusion in the context of the problem.
Answer:
[tex]t=\frac{30.8-30}{\frac{1.5}{\sqrt{32}}}=3.017[/tex]
[tex]p_v =2*P(t_{(31)}>3.017)=0.0051[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the treu mean is different from 30 minutes at 1% of significance
Step-by-step explanation:
Data given and notation
[tex]\bar X=30.8[/tex] represent the sample mean
[tex]s=1.5[/tex] represent the sample standard deviation
[tex]n=32[/tex] sample size
[tex]\mu_o =30[/tex] represent the value that we want to test
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
1) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is equal to 30 minutes, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 30[/tex]
Alternative hypothesis:[tex]\mu \neq 30[/tex]
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
2) Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{30.8-30}{\frac{1.5}{\sqrt{32}}}=3.017[/tex]
3) P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=32-1=31[/tex]
Since is a two sided hypothesis test the p value would be:
[tex]p_v =2*P(t_{(31)}>3.017)=0.0051[/tex]
4) Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the treu mean is different from 30 minutes at 1% of significance
MATH 1325 – EXAM 4 NAME: ______________________________ SHOW ALL WORK. ANSWERS WITHOUT WORK WILL RECEIVE NO CREDIT. YOU MUST USE A PENCIL. READ ALL DIRECTIONS. POINTS WILL BE DEDUCTED FOR FAILURE TO FOLLOW DIRECTIONS. TRUE/FALSE – WRITE THE WORD THAT BEST DESCRIBES THE GIVEN STATEMENT BY WRITING EITHER "TRUE" OR "FALSE" IN THE SPACE PROVIDED TO THE LEFT OF THE PROBLEM. __________ 1. THE ABSOLUTE MAXIMUM OF A FUNCTION ALWAYS OCCURS WHERE THE DERIVATIVE HAS A CRITICAL FUNCTION. __________ 2. IMPLICIT DIFFERENTIATION CAN BE USED TO FIND dy dx WHEN x IS DEFINED IN TERMS OF y . __________ 3. IN A RELATED RATES PROBLEM, THERE CAN BE MORE THAN TWO QUANTITIES THAT VARY WITH TIME. __________ 4. A CONTINUOUS FUNCTION ON AN OPEN INTERVAL DOES NOT HAVE AN ABSOLUTE MAXIMUM OR MINIMUM. __________ 5. IN A RELATED RATES PROBLEM, ALL DERIVATIVES ARE WITH RESPECT TO TIME. MULTIPLE CHOICE – CHOOSE THE ONE ALTERNATIVE THAT BEST COMPLETES THE STATEMENT OR ANSWERS THE QUESTION BY CIRCLING THE CORRECT LETTER. 6. FIND THE MAXIMUM ABSOLUTE EXTREMUM AS WELL AS ALL VALUES OF x WHERE IT OCCURS ON THE SPECIFIED DOMAIN
True, True, True, False, True. Without the multiple-choice question options, I can't provide a specific response.
Let's address each question and provide the appropriate response:
1. True/False: "The absolute maximum of a function always occurs where the derivative has a critical function."
- Answer: False. The absolute maximum of a function can occur at critical points, but it can also occur at endpoints of the domain or other non-critical points.
2. True/False: "Implicit differentiation can be used to find \( \frac{dy}{dx} \) when \( x \) is defined in terms of \( y \)."
- Answer: True. Implicit differentiation is a technique used to find derivatives of functions that are not explicitly defined in terms of one variable.
3. True/False: "In a related rates problem, there can be more than two quantities that vary with time."
- Answer: True. Related rates problems involve the rates of change of multiple quantities that are related to each other through an equation or situation.
4. True/False: "A continuous function on an open interval does not have an absolute maximum or minimum."
- Answer: False. A continuous function on a closed interval always has an absolute maximum and minimum by the Extreme Value Theorem.
5. True/False: "In a related rates problem, all derivatives are with respect to time."
- Answer: True. Related rates problems involve finding rates of change with respect to time.
Multiple Choice:
6. Since the multiple-choice question is not provided, I can't offer a response. If you have the options, feel free to share them, and I can help you choose the correct one.