Using Chebyshev's theorem, we conclude that at least 88.9% of recent graduates have salaries between $22,800 and $30,000, given a mean salary of $26,400 and a standard deviation of $1200.
Explanation:The question is asking for the minimum percentage of recent graduates who have salaries within a specific range using Chebyshev's Theorem. By definition, Chebyshev's theorem states that at least 1 - 1/k^2 of data from a sample will fall within k standard deviations from the mean, where k is any number greater than 1. The range in this question can be represented as being within 3 standard deviations from the mean (because ($30,000 - $26,400)/$1200 = 3 and ($26,400 - $22,800)/$1200 = 3). Thus, the minimum percentage of recent graduates having salaries within this range is at least 1 - (1/3^2) = 1 - 1/9 = 8/9 = 88.9%. So, at least 88.9% of the recent graduates fall within this salary range according to Chebyshev's theorem.
Learn more about Chebyshev's Theorem here:https://brainly.com/question/34274356
#SPJ3
6. Active is an energy drink that claims to provide physical strength. To test this claim, the
producers of Active conducted a study. The company recruited 25 high school athletes and 4
professional football players to participate in the study. The high school athletes were each
randomly assigned to drink between 1 and 5 ounces of Active. The professional football
players were assigned to drink either 30 or 31 ounces. After waiting 10 minutes they
completed as many pull-ups as they could. Here is a scatterplot showing the number of
energy drinks consumed and the number of pull ups that were completed by each participant,
as well as a line of best fit.
Which of the following would increase if
the professional football players were
removed from the data set?
umber of Pull Ups
(A)r
(B)r^2
(C) the slope
(D) the standard deviation of the residuals
(E) None of the above.
Answer:
D) The standard deviation of the residuals
Step-by-step explanation:
Solve the proportion. 5/7=x/35
Answer:
x = 25
Step-by-step explanation:
[tex] \frac{5}{7} = \frac{x}{35} \\ \\ x = \frac{5 \times 35}{7} \\ \\ x = 5 \times 5 \\ \\ \huge \red{ \boxed{ x = 25}}[/tex]
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 270 days and a standard deviation of 8 days. (a) What is the minimum pregnancy length that can be in the top 8% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 3% of pregnancy lengths?
Answer:
a) 281 days.
b) 255 days
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 270, \sigma = 8[/tex]
(a) What is the minimum pregnancy length that can be in the top 8% of pregnancy lengths?
100 - 8 = 92th percentile.
X when Z has a pvalue of 0.92. So X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 270}{8}[/tex]
[tex]X - 270 = 1.405*8[/tex]
[tex]X = 281[/tex]
(b) What is the maximum pregnancy length that can be in the bottom 3% of pregnancy lengths?
3rd percentile.
X when Z has a pvalue of 0.03. So X when Z = -1.88
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.88 = \frac{X - 270}{8}[/tex]
[tex]X - 270 = -1.88*8[/tex]
[tex]X = 255[/tex]
a racetrack is 40 yards long. How many feet is that?
Answer:
120 feet in total
Step-by-step explanation:
Hi there! I'm glad I was able to help you out!
We are given that one racetrack is 40 yards long in length.
We also know that there are three feet in one yard alone. In order to get the answer to this math problem, all we have to do is multiply 40 by 3, where the 40 represents the amount of yards and the 3 represents the amount of feet IN a single yard.
40 × 3 = 120
Therefore, there are 120 feet in total, in terms of the racetrack's length.
I hope I was able to help you understand this a little bit more! :)
There are 120 feet in total, in terms of the racetrack's length.
Here, we have,
a racetrack is 40 yards long.
we know that,
1 yard = 3 feet
We are given that one racetrack is 40 yards long in length.
We also know that there are three feet in one yard alone.
In order to get the answer to this math problem, all we have to do is multiply 40 by 3,
where the 40 represents the amount of yards
and the 3 represents the amount of feet IN a single yard.
40 × 3 = 120
Therefore, there are 120 feet in total, in terms of the racetrack's length.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ6
What’s 0.798 as a percent
Answer:
The answer would be, 79.8%.
-Hope this helps! :D
Answer:
[tex]0.798\%[/tex]
Step-by-step explanation:
[tex]0.798 \times 100\% \\ 0.798 \times \frac{100}{100} \\ = \frac{0.798 \times 100}{100} \\ = 0.798\%[/tex]
Test the set of functions for linear independence in ℱ. If it is linearly dependent, express one of the functions as a linear combination of the others. (If the set is linearly independent, enter INDEPENDENT. If the set is linearly dependent, enter your answer as an equation using the variables f, g, and h as they relate to the question.) {f(x) = 8, g(x) = sin(x), h(x) = cos(x)}
Answer:
Linearly independent
Step-by-step explanation:
let a,b,c be element of F. for all x element of F.
1) if a, b and c are zero then they are independent
2) if not all a,b,c are zero then it is independent.
Now lets write it as a linear combination
i.e 8a +b Sinx +c Cosx = 0
equating the coefficients we have
: 8a =0 hence a = 0
: b Sinx = 0
b = 0
: c Cos x = 0
c is not 0
Hence it is Linearly independent
Final answer:
Linearly test the set {f(x) = 8, g(x) = sin(x), h(x) = cos(x)} for independence. If dependent, express one function as a combination of others.
Explanation:
To test for linear independence in the set ℱ = {f(x) = 8, g(x) = sin(x), h(x) = cos(x)}, we can see if the determinant of the matrix formed by the functions is zero. If it is, the set is linearly dependent. If the set is linearly dependent, we can write one function as a linear combination of the others, for example, h(x) = √(g(x)^2 + f(x)^2).
Let a1equals=[Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 2 3rd Row 1st Column negative 1 EndMatrix ]1 2 −1 , a2equals=[Start 3 By 1 Matrix 1st Row 1st Column negative 6 2nd Row 1st Column negative 5 3rd Row 1st Column 3 EndMatrix ]−6 −5 3 , and bequals=[Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 8 3rd Row 1st Column h EndMatrix ]3 −8 h . For what value(s) of h is b in the plane spanned by a1 and a2?
Answer:
Check attachment for solution
Step-by-step explanation:
Given that,
suppose 42 stamps are added to a stamp collection that has 30 stamps
Answer:
if you are trying to find the total amount of stamps its 72 stamps
Step-by-step explanation:
calculator
(19.28) To estimate the mean score μ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.6. You want your sample mean x¯¯¯ to estimate μ with an error of no more than 1.4 point in either direction.
What standard deviation (±0.0001) must x¯ have so that 99.7% of all samples give an x¯ within 1.4 point of μ?
Answer:
standard deviation = ±0.4667
Step-by-step explanation:
In Normal distribution, approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.
Therefore, for a confidence interval of 99.7% the standard deviation of the x¯ must be 3 standard deviations from the mean,
3σ = ±1.4
σ = ±1.4/3
σ = ±0.4667
Therefore, 0.4667 is the standard deviation that x¯ must have so that 99.7% of all samples give an x¯ within 1.4 point of μ.
According to researchers, a coin flip may not have a 50% chance of landing heads and a 50% chance of landing tails. In fact, they believe that a coin is more likely to land the same way it started. So if it starts out heads up, it is more likely to land heads up. Suppose someone tests this hypoth- esis with 1,000 flips of a coin where it starts out heads up each time. a. Describe what the symbol a stands for in this context. b. State your null and alternative hypotheses. c. Suppose 52% of the sample of 1,000 flips landed heads facing up. Verify the validity conditions that allow us to use a theory-based test. d. A theory-based test reports a standardized statistic of 1.26. Interpret what this means. e. A theory-based test reports a p-value of 0.1030. State your conclusion in terms of strength of evidence and what that means in the context of the study.
Answer:
a) π = np
π represents the number of heads that turn up in 1000 tosses of the coin.
b) The null hypothesis is represented as
H₀: p ≤ 0.50
The alternative hypothesis is given as
Hₐ: p > 0.50
c) The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.
The validity conditions are met because we have 1000 tosses with 520 heads and 480 tails, indicating that we have more than 20 sample size in this sample.
The sample proportion (0.52) and the standard error of the sample proportion (0.0158) show that the distribution approximates a normal distribution and isn't skewed. So, the theory based test for this study is valid.
d) Check Explanation
e) The p-value obtained is greater than the significance level at which the test might have been performed, hence, we fail to reject the null hypothesis and conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
The researchers' claim then has to be wrong.
Step-by-step explanation:
a) If p corresponds to the proportion of 1000 tosses that turn up heads,
π = np
where n = number of tosses.
b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question where we want to verify that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head. That is, the proportion of heads in multiple tosses is more than 0.5 given that the first toss was a head.
The null hypothesis would be that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
That is, the coin is likely to turn up heads less than or equal to 50% of the time, when it is tossed multiple times, starting with a first toss that gives a head.
The alternative hypothesis is that there is significant evidence to conclude that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
Mathematically,
The null hypothesis is given as
The null hypothesis is represented as
H₀: p ≤ 0.50
The alternative hypothesis is given as
Hₐ: p > 0.50
c) The conditions that need to be satisfied before a theory based test is used include:
The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.
d) The standardized statistic shows how far away from the standard proportion (the proportion that the population proportion is being compared with) the sample proportion is in terms of the standard error of the sample proportion.
It is given mathematically as,
t or z = (x - μ)/σₓ
x = p = sample proportion of the number of heads obtained in the multiple tosses starting with a first result of a head turning up = 0.52
μ = p₀ = 0.50 (the standard being tested against.
σₓ = standard error of the sample proportion, given as σₓ = √[p(1-p)/n]
n = sample size = 100
σₓ = 0.0158
The standardized statistic is also used to obtain the p-value that indicates how significant the results of the theory based test is.
e) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, like all other hypothesis testing, the significance level is usually at 0.05. On rare occasions, 0.01 and 0.10 are often used.
Whichever of the 3 is used,
p-value = 0.1030
0.1030 > 0.05, 0.01 or 0.10
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
Hope this Helps!!!
Cecil solved a theoretical prediction problem, where a spinner would be spun 30 times. She correctly concluded: “The spinner will land on the red section 6 times.” What could the spinner look like? Is there more than one possible solution?
6 out of 30 times would be written as
6/30 which reduces to 1/5 which would mean the spinner is divided into 5 different colors.
There could be more than one solution. The spinner could be divided into 10 spaces and red could be 2 of the spaces, or any other multiple of 5s
Answer:
The spinner has 5 equal sections, with one section red.
It can have 5N equal sections, with N sections Red
Step-by-step explanation:
p(red) = 6/30 = 1/5
1/5 = 2/10
Out of 10 sections, 2 are Red
In general,
It can have 5N equal sections, with N sections Red
The mean number of miles driven per vehicle annually in the United States is 12,494 miles. Choose a randomly selected vehicle, and assume the annual mileage is normally distributed with a standard deviation of 1290 miles. Would you buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year
No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year and this can be determined by using the formula of z-score.
Given :
The mean is 12,494 miles. The standard deviation of 1290 miles.The following steps can be used in order to determine whether you have to buy a vehicle or not:
Step 1 - The formula of z-score can be used in order to determine whether you have to buy a vehicle or not.
Step 2 - The z-score formula is given below:
[tex]\rm z = \dfrac{x-\mu}{\sigma}[/tex]
Step 3 - Substitute the known terms in the above expression.
[tex]\rm z = \dfrac{6000-12494}{1290}=-5.0341[/tex]
Step 4 - Now, the p-value is given below:
[tex]\rm P(x < 6000)=P(z<-5.0341)[/tex]
Step 5 - Now, using the z table the value of P is:
P(x < 6000) = 0
No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year.
For more information, refer to the link given below:
https://brainly.com/question/13299273
What situation could be modeled with the equation 40÷8=5
The required situation could be modeled with the equation 40 ÷ 8 = 5 as "There are eight in each of the 40 groups. Which groupings are there, exactly?"
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
The equation is given in the question
40 ÷ 8 = 5
An equation of this kind may be used to model any situations in which 40 items are divided into 8 or 5 divisions. There are a few possibilities:
"There are eight in each of the 40 groups. Which groupings are there, exactly?"
"There are a total of 40, separated into 8 categories. In how many groups are there?"
Thus, the above situations could be modeled with the equation 40 ÷ 8 = 5.
To learn more about the division operation click here :
brainly.com/question/25870256
#SPJ5
The price of a home is 240,000. The bank requires a 20% down payment and two points at the time of closing. The cost of the home is financed with a 30 year fixed rate mortgage at 7%. Find the amount of the mortgage. How much must be paid for the two points at closing?
Final answer:
The mortgage amount for the home is $192,000 after a 20% down payment on a $240,000 purchase price. The cost for two points at closing is $3,840, which is 2% of the mortgage amount.
Explanation:
The amount of the mortgage can be found by subtracting the 20% down payment from the purchase price of the home. For a home priced at $240,000, a 20% down payment is $48,000 ($240,000 × 0.20), leaving a mortgage amount of $192,000 ($240,000 - $48,000).
Next, the cost of the two points at closing is calculated based on the mortgage amount. Each point costs 1% of the mortgage amount, so two points would be 2% of $192,000, which comes to $3,840
Kevin has an equal number of dimes, nickel and quarters in his piggy bank. He randomly picks a coin, replaces it, and picks another coin. What is the probability that the sum of the two coins is at least 30cents?
Answer:
5/9
Step-by-step explanation:
Justin plans to attend a four-year college. He has
estimated the costs per year.
I Tuition = $2,900
Justin's plan doesn't cover his costs completely. What
are his options for covering the rest of his costs? Select
all that apply.
He could try to save more money.
He could get a student loan for the extra amount he
needs.
Other educational expenses = $280
Housing and living expenses = $4,100
Justin's counselor estimates he will receive $3,500 a
year in grants. He also will be eligible for a work-study
program that pays $2,800 per year. Justin also plans to
save enough money to contribute $500 each year.
He could apply for a scholarship.
He could ask his friends to loan him money.
He could ask his family to contribute.
Answer:
a, b. c, e
Step-by-step explanation:
Hence, Justin will have to ask for 1480 from family and friends to cover cost.
What is cost?
Amount at which any product prices , that is it can be sold or bought.
How to calculate?
I Tuition = -$2,900
Other educational expenses = -$280
Housing and living expenses =- $4,100
estimates of grants= $3,500
work-study program =$2,800
savings = $500
hence cost = 3500-2900-280-4100+2800-500=-1480
∴ Justin will have to ask for 1480 from family and friends to cover cost.
Learn more about cost
https://brainly.com/question/1153322
#SPJ2
) The data below represent the weight losses for people on three different exercise programs. Exercise A 2.5 8.8 7.3 9.8 5.1 Exercise B 5.8 4.9 1.1 7.8 1.2 Exercise C 4.3 6.2 5.8 8.1 7.9 At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs
Answer:
See attached files
Step-by-step explanation:
Plz help asap!!!!!!!!!!!!!!!!!!!!
Answer:
C) ⅙
Step-by-step explanation:
Starting with A:
April, August
2/12
1/6
Pam’s annual gross pay is $48,000. If she is paid biweekly, what is her gross pay on each pay check?
Answer:
$2000
Step-by-step explanation:
biweekly is defined as every 2 weeks
assume each month has 4 weeks
there are 12 months in a year and she is paid 2x per month so there are 24 weeks she is paid
48000/24 can be used to find the biweekly pay which is 2000
Pam's gross pay per biweekly paycheck is calculated by dividing her annual salary ($48,000) by the number of pay periods in a year (26). This results in an approximate gross pay of $1,846.15 per biweekly paycheck.
Explanation:The student's question pertains to calculating her gross pay per paycheck given her annual salary. To carry out this process, you need to understand that there are typically 52 weeks in a year and that being paid biweekly results in 26 pay periods (52 weeks divided by 2). Hence, you divide Pam’s annual gross pay amount of $48,000 by the 26 pay periods to get her gross pay, per paycheck.
Steps:
Identify the number of pay periods in a year, which in this case is 26 because she is paid biweekly (every two weeks).Divide the annual salary by the number of pay periods.The result is the gross pay per paycheck.So, $48,000 / 26 = $1,846.15
This means Pam's biweekly paycheck would be roughly $1,846.15, before taxes and other deductions.
https://brainly.com/question/32331850
#SPJ2
The number of hours between successive train arrivals at the station is uniformlydistributed on [0;1]. Passengers arrive according to a Poisson process with rate 7 perhour. Suppose a train has just left the station. LetXdenote the number of peoplewho get on the next train. Denote byTthe arrival time of the next train.(a)GivenT= 0:4, what is the conditional expectationE(XjT= 0:4).(b)FindE(X). Hint: useE(X) =E[E(XjT)].
Answer:
E ( X ) = 3.5
Var ( X ) = 91 / 12
Step-by-step explanation:
Solution:-
- Let X = M (T), where M (T) is the Random variable that denotes the number of arrivals in time T for the Poisson process. The parameter λ = rate of 7 per hour
- To find E ( X ), condition X on the random arrival time T of the next train.
- Note that if Y ~ Poisson ( μ ), then the T is defined by uniform distribution over the interval [ 0 , 1 ] :
E ( Y ) = Var ( Y ) = μ
E ( T ) = 1 / 2
Var ( T ) = 1 / 12
- We have, N ( T ) ~ Poisson ( λt ), where t ≥ 0 and λ = 7. Thus,
E ( N ( T ) / T ) = λ*T
Var ( N ( T ) / T ) = λ*T.
Therefore,
E ( X ) = E ( N ( T ) ) = E ( E ( N ( T ) / T ) )
= E ( λ*T ) = λ* E ( T ) = 7/ 2 = 3.5
- For two Random Variables U and V,
Var ( U ) = E ( Var ( U / V ) ) + Var ( E ( U / V ) )
Therefore,
Var ( X ) = E ( Var ( X / T ) ) + Var ( E ( N ( T ) / T ) )
= E ( λ*T) + Var ( λ*T )
= λ* E ( T ) + λ^2* Var ( T )
= 3.5 + 7^2 / 12
= 91 / 12
If 3612 – m – 62m, what is the value of m?
LEO
ООО
о со од
Answer:
3612 - 63 m
Step-by-step explanation:
3612 – m – 62m
We cannot find the value of m, but we can simplify the expression
3612 – m – 62m
3612 - 63 m
To find the value of m, we can solve the given equation: 3612 - m - 62m. Combining the m terms, we have: 3612 - 63m. Since no other operations are indicated, we assume this is an equation and set it equal to zero. Now, let's solve for m: Subtracting 3612 from both sides, -63m = -3612. Dividing both sides by -63, m = 57.33.
Explanation:To find the value of m, we can solve the given equation:
3612 - m - 62m
Combining the m terms, we have:
3612 - 63m
Since no other operations are indicated, we assume this is an equation and set it equal to zero:
3612 - 63m = 0
Now, let's solve for m:
Subtracting 3612 from both sides:
-63m = -3612
Dividing both sides by -63:
m = 57.33
Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = −sin x, [0, π] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
Answer with Step-by-step explanation:
We are given that
[tex]f(x)=-sin x[/tex]
[tex][0,\infty][/tex]]
Average value of the function is given gy
[tex]f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx=\frac{1}{\pi-0}\int_{0}^{\pi}-sinx dx[/tex]
[tex]f_{avg}=\frac{1}{\pi}[cosx]^{\pi}_{0}[/tex]
Using the formula
[tex]\int sin xdx=-cos x[/tex]
[tex]f_{avg}=\frac{1}{\pi}(cos\pi-cos0)[/tex]
[tex]f_{avg}=\frac{1}{\pi}(-1-1)=-\frac{2}{\pi}[/tex]
[tex]f(x)=f_{avg}[/tex]
[tex]-sinx=-\frac{2}{\pi}[/tex]
[tex]sinx=\frac{2}{\pi}[/tex]
[tex]x=sin^{-1}(\frac{2}{\pi})=0.69radian[/tex]
The average value of the function is [tex]-\frac{2}{\pi}[/tex].
Average value :The average value of the function is given as,
[tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {f(x)} \, dx[/tex]
Given function is, [tex]f(x)=-sinx[/tex]
Substitute values in above relation.
[tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {-sinx} \, dx\\\\Average=\frac{1}{\pi} (cosx)^{\pi} _{0}\\\\Average=\frac{1}{\pi}(cos\pi - cos 0)\\\\Average=\frac{1}{\pi}(-1-1)\\\\Average=-\frac{2}{\pi}[/tex]
The values of x in the interval for which the function equals its average value is,
[tex]-sinx=-\frac{2}{\pi}\\ \\x=sin^{-1} (\frac{2}{\pi} )=39.56[/tex]
Learn more about the average value of function here:
https://brainly.com/question/20118982
A scale drawing of an apartment is shown. What are the actual dimensions of the Living Space?
Answer: 12 Centimeter
Step-by-step explanation:
3 by 4 multiplied by 2
3cm x 4cm x 2
= 12cm x 2
= 24cm
Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of 3 ml. A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4 297.7 301.0 298.9 300.2 297.0 Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? Test at the 5% significance level.
Answer:
We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.
Step-by-step explanation:
We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.
A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0
Let [tex]\mu[/tex] = mean contents of cola bottles.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 300 ml {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 300 ml {means that the mean contents of cola bottles is less than the advertised 300 ml}
The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean contents of cola bottle = [tex]\frac{\sum X}{n}[/tex] = 299.03 ml
[tex]\sigma[/tex] = population standard deviation = 3 ml
n = sample of bottles = 6
So, test statistics = [tex]\frac{299.03-300}{\frac{3}{\sqrt{6} } }[/tex]
= -0.792
Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.
Answer:
b its b i am a student i got good grades very goods grades
Step-by-step explanation:
Show how to solve (3X+2)-(2X-1)
what is the equation of the line that passes through the point (-2,-2)and has a slope of 2
Answer:
y=2x+2
Step-by-step explanation:
To find the y intercept of the equation you add 4 beacuse the point is 2 under the y intecrept and 2*2 is 4 so -2+4=2 so the y value of the y intercept is 2 so
y=2x+2
Answer:
y=2x+2
Step-by-step explanation:
Since we have a point and a slope, we can use the point slope formula:
y-y1=m(x-x1)
where m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point
We know the slope is 2, the y coordinate is -2, and the x coordinate is also -2, so we can substitute them in
y-y1=m(x-x1)
y- -2 =2(x - -2)
y+2=2(x+2)
Now we need to solve for/ isolate y
Distribute the 2
y+2=2*x+2*2
y+2=2x+4
Subtract 2 from both sides
y=2x+2
Variables x and y are in direct proportion, and y = -12 when x = -3. Which line in the graph correctly shows the relationship between x and y?
Answer:
Line C
Step-by-step explanation:
I picked this answer because the slope of the line is 4, which is -12/-3.
If this answer is correct, please make me Brainliest!
You have been given the task of finding out what proportion of students that enroll in a local university actually complete their degree. You have access to first year enrolment records and you decide to randomly sample 115 of those records. You find that 85 of those sampled went on to complete their degree.
a)Calculate the proportion of sampled students that complete their degree. Give your answer as a decimal to 2 decimal places
Calculate lower bound and upper bound at 95% confidence interval. Give answer decimal to 3 places.
Answer:
The proportion of sampled students that complete their degree is 0.74.
The lower bound for the 95% confidence interval is 0.659 and the upper bound is 0.819.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 115, \pi = \frac{85}{115} = 0.739[/tex]
Rounded to two decimal places, the proportion of sampled students that complete their degree is 0.74.
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.739 - 1.96\sqrt{\frac{0.739*0.261}{115}} = 0.659[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.739 + 1.96\sqrt{\frac{0.739*0.261}{115}} = 0.819[/tex]
The lower bound for the 95% confidence interval is 0.659 and the upper bound is 0.819.
Determine which of the following are equivalence relations and/or partial ordering relations for the given sets: A = { lines in the plane } , and r defined by x r y if and only if x is parallel to y . Assume every line is parallel to itself. A = R and r defined by x r y if and only if | x − y | ≤ 7
Answer:
Check the explanation
Step-by-step explanation:
1
a) A is an Equivalence Relation
Reflexive : x is parallel to itself => x R x
Symmetric : x is parallel to y => y is parallel to x.
Therefore x R y => y R x
Transitive : x is parallel to y and y is parallel to z then x, y, z are parallel to each other.
=> x R y and y R z => x R z
Therefore A is equivalent.
1. b)
x r y if and only if |x-y| less than or equal to 7
Reflexive : |x-x| = 0 <= 7 => x R x Satisfied.
Symmetric : let x R y => |x-y| <= 7
Consider |y-x| = |(-1)*(x-y)| = |x-y| <= 7
=> y R x => Satisfied
Transitive : let x R y and y R x
=> |x-y| <= 7 and |y-z| <= 7
but this doesn't imply x R z
Counter-Example : x = 1, y = 7, z = 10
Therefore this relation is neither Equivalent nor Partial Order Relation.
The relation x r y if and only if x is parallel to y for lines in the plane is an equivalence relation as it is reflexive, symmetric, and transitive. For the set of real numbers with the relation x r y if and only if |x - y| ≤ 7, the relation is neither an equivalence relation nor a partial ordering because it lacks antisymmetry.
Explanation:When determining if a relation is an equivalence relation or a partial ordering, we must assess whether it satisfies specific properties. For a relation to be an equivalence relation, it must be reflexive, symmetric, and transitive. In the case of A = { lines in the plane } and relation r defined by x r y if and only if x is parallel to y, we can say:
Reflexive: Every line is parallel to itself by assumption.Symmetric: If line x is parallel to line y, then line y is also parallel to line x.Transitive: If line x is parallel to line y, and line y is parallel to line z, then line x is parallel to line z.Therefore, this relation is an equivalence relation.
For the set A = R and the relation r defined by x r y if and only if | x − y | ≤ 7, the relation is not a partial ordering because it is not antisymmetric (if x r y and y r x, then x must equal y, which isn't necessarily true for all real numbers within 7 units of each other). However, it is reflexive and symmetric.
According to a recent census, 14.6% of all housing units in a certain country are vacant. A county supervisor wonders if her county is different from this. She randomly selects 865 housing units in her county and finds that 159 of the housing units are vacant.
Name the model and check appropriate conditions for a hypothesis test. What kind of test is this?
A. One-proportion z-test
B. Two-proportion t-test
C. Proportional t-test
D. Difference in proportions test
Answer:
We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:
Null hypothesis:[tex]p=0.146[/tex]
Alternative hypothesis:[tex]p \neq 0.146[/tex]
A. One-proportion z-test
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And the conditions required are:
1) The data comes from a random sampling
2) Independence condition between observations
3) np>10 and n(1-p)>10
4) The sample size is 10 times lower than the population size.
Step-by-step explanation:
Data given and notation
n=865 represent the random sample taken
X=159 represent the housing units that are vacant
[tex]\hat p=\frac{159}{865}=0.184[/tex] estimated proportion of vacant units
[tex]p_o=0.146[/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)
Solution to the problem
We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:
Null hypothesis:[tex]p=0.146[/tex]
Alternative hypothesis:[tex]p \neq 0.146[/tex]
A. One-proportion z-test
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And the conditions required are:
1) The data comes from a random sampling
2) Independence condition between observations
3) np>10 and n(1-p)>10
4) The sample size is 10 times lower than the population size.