On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. Using the Poisson distribution, the probability that five cars will arrive during the next five minute interval is _____________.

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 25 who smoke.

Step 1 of 2: Suppose a sample of 2017 Americans over 25 is drawn. Of these people, 564 smoke. Using the data, estimate the proportion of Americans over 25 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Step 2 of 2:

Suppose a sample of 2017 Americans over 25 is drawn. Of these people, 564 smoke. Using the data, construct the 95% confidence interval for the population proportion of Americans over 25 who smoke. Round your answers to three decimal places.

A particular fruit's weights are normally distributed, with a mean of 336 grams and a standard deviation of 11 grams.

If you pick 17 fruit at random, what is the probability that their mean weight will be between 331 grams and 345 grams? State your answer to four decimal places.

Sixty percent of dogs from a certain breed will chase a thrown ball. In a group of 15 dogs of this breed,

What’s the probability that less than 10 will chase a ball?

What’s the probability that at least 12 will chase a ball?

What’s the probability that exactly 8 will chase a ball?

What’s the probability that at most 4 will not chase a ball?

Discuss the bases for the selection of the statistical treatment to be used.

A coin with probability of heads equal to .6 is tossed a first series of 10 tosses.

Let X be the number of heads and let Y be the number of tails obtained.

(a) (1 POINT) Argue with a short sentence that the covariance Cov(X, Y) should be negative.
(b) (1 POINT) Find Cov(X,Y).

In a second series of tosses, the same coin is tossed as many times as the number of heads in the first series.

(c) (3 POINTS) Find the expected number of heads in the first and second series of tosses.

(d) (3 POINTS) Find the probability that the number of heads in the second series is 0.

4) A magazine reported the results of a survey in which readers were asked to send their responses to several questions regarding good eating. DataSet for question 4,5,6 is the reported results to the question, How often do you eat chocolate? Based on the data answer the following questions.

a) Were the responses to this survey obtained using voluntary sampling technique? Explain

b) What type of bias may be present in the response?

c) is 13% a reasonable estimate of the proportion of all Americans who eat chocolate frequently? Explain.

5) A magazine reported the results of a survey in which readers were asked to send in their responses to several questions regarding anger. DataSet2 for Question 5 shows the reported results to the question, How long do you usually stay angry? Answer the following questions based on the data.

a) Were the responses to this survey obtained using voluntary sampling technique?

b) What type of bias may be present in the response?

c) Is 22% a reasonable estimate of the proportion of all Americans who hold a grudge indefinitely? Explain.

6) Students in marketing class have been asked to conduct a survey to determine whether or not there is demand for an insurance program at a local college. The Students decided to randomly select students from the local college and mail them a questionnare regarding the insurance program. Of the 150 questionnaire that were mailed, 50 students responded to the following survey item: Pick the Category which best describes your interest in an insurance program. DataSet2 for question 6 shows the responses. Use this data to answer the following question.

a)What type of bias may be present in the response?

b) is 50% a reasonable estimate of the proportion of all students who would be very interested in an insurance program at a local college? Explain.

c) is 50% a reasonable estimate of the proportion of all business majors who would be very interested in an insurance program at a local college? Explain.

d) What strategies do you think the marketing students could have used in order to get a less biased response to their survey?

e) Suppose the program was created and only a few people registered. How could the survey question have been reworded to better predict the actual enrollment?

DATA SET FOR QUESTION 4, 5 AND 6

Table for Question 4 – Survey Responses

Category % of Responses

Frequently 13

Occasionally 45

Seldom 37

Never 5

Table for Question 5 – Survey Responses

Category % of Responses

A few hours or less 48

A day 12

Several days 9

A month 1

I hold a grudge indefinitely 22

It depends on the situation 8

Table for Question 6 – Survey Responses
Category % of Responses
Very Interested 50
Somewhat Interested 15
Interested 10
Not Very Interested 5
Not At All Interested 20

CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 242 dollars. You take a simple random sample of 89 auto insurance policies.

Find the probability that a single randomly selected value is at least 980 dollars.
P(X > 980) =

Find the probability that a sample of size n=89n=89 is randomly selected with a mean that is at least 980 dollars.
P(M > 980) =

Enter your answers as numbers accurate to 4 decimal places.

Mean=33,820.21

Standard Deviation=22,948.45

n=52

Calculate a 99% confidence interval, assuming that sigma is unknown.

A study was performed to test a new treatment for autism in children. In order to test the new method,

parents of children with autism were asked to volunteer for the study in which 9 parents volunteered their

children for the study. The children were each asked to complete a 20 piece puzzle. The time it took to

complete the task was recorded in seconds. The children then received a treatment (20 minutes of yoga) and

were asked to complete a similar but different puzzle. The data from the study is below:

Child Before After

1 85 75

2 70 60

3 40 50

4 65 40

5 80 20

6 75 65

7 55 40

8 20 25

9 70 30

Part A

Calculate the statistic S for a signed rank test by hand showing the final table with the absolute differences,

the signs, and the ranks. Also, show your calculation of the z-statistic (standardized S statistic).

Part B

Verify your calculation in both SAS and R. Simply cut and paste your code and relevant output.

Part C

Using all the information from parts A and B, conduct the six step hypothesis test using your calculations

from above to test the claim that the yoga treatment was effective in reducing the time to finish the puzzle.

Part D

Use SAS to conduct a six step hypothesis test using a paired t-test to test the claim that the yoga treatment

was effective in reducing the time to finish the puzzle.

Part E

Verify your calculations in R. Simply cut and paste your code and relevant output.

Part F

Which test (the sign test, the signed rank test, or the paried t-test) do you think is most appropriate for this

data? Why?

Consider the accompanying data on plant growth after the application of different types of growth hormone. 1: 13 16 7 13 2: 20 12 19 16 3: 19 16 20 16 4: 7 11 18 9 5: 6 10 15 9 (a) Perform an F test at level α = 0.05. State the appropriate hypotheses. H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 Ha: all five μi's are equal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 Ha: at least two μi's are equal H0: μ1 = μ2 = μ3 = μ4 = μ5 Ha: all five μi's are unequal H0: μ1 = μ2 = μ3 = μ4 = μ5 Ha: at least two μi's are unequal Calculate the test statistic. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Fail to reject H0. There appears to be a difference in the average growth of at least two groups. Reject H0. There appears to be a difference in the average growth of at least two groups. Reject H0. There does not appear to be a difference in the average growth. Fail to reject H0. There does not appear to be a difference in the average growth. (b) What happens when Tukey's procedure is applied? (Round your answer to two decimal places.) w = Which means differ significantly from one another? (Select all that apply.) x1. and x2. x1. and x3. x1. and x4. x1. and x5. x2. and x3. x2. and x4. x2. and x5. x3. and x4. x3. and x5. x4. and x5. There are no significant differences. Are Tukey's method and the F test in agreement? Yes No

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 146 eligible voters aged​ 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged​ 18-24, 22% of them voted.

Probability that fewer than 37 voted

Are older men shorter than younger men? According to a national report, the mean height for U.S. men is 69.4 inches. In a sample of 119 men between the ages between of 60 and 69 and, the mean height was 69.3 inches. Public health officials want to determine whether the mean height for older men is less than the mean height of all adult men. Assume the population standard deviation to be 2.58. Use the a=0.05 level of significance and the-value method with the table.

A researcher wanted to test the claim that members of college sororities have grade point averages (GPA) above the mean GPA of 2.64 for all college students. She collected a random sample of 50 members of college sororities that had a mean GPA of 2.82. It is known that the population standard deviation for GPA is 0.90. Conduct a hypothesis test for this situation at the 0.05 level of significance and indicate what the researcher should conclude.

For the following, indicate whether you should use a one sample t-test, paired t-test, or two sample t-test and whether you have chosen a one-sided or two-sided alternate hypothesis:

A) Do macroeconomics students at Vanderbilt score significantly higher on the Math SAT than the national average?

My Answer: One sample t-test, one tailed

B) Do macroeconomics students at Vanderbilt score significantly higher on the Verbal SAT than the national average?

My answer: One sample t-test, one tailed

C) Report a 95 percent confidence interval for the true mean Math SAT score. Do 95 percent of students have Math SAT scores that fall within this interval? Explain your answer.

My answer: One sample t-test, one tailed

D) Is there a statistically significant difference between the Verbal and Math scores of macroeconomics students at Vanderbilt?

My Answer: Paired t-test, two tailed

E) Is there a statistically significant difference between the performances of males and females on the Verbal SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My Answer: Two sample t-test, two tailed

F) Is there a statistically significant difference between the performances of males and females on the Math SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My answer: Two sample t-test, two tailed

G) Is there a statistically significant difference between the freshman GPAs of males and females? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My answer: Two sample t-test, two tailed

Could someone please double check my answers and if any are incorrect, explain to me where I went wrong? Thanks!