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!

Suppose there is a linear association between crime rate and percentage of high school graduates.

a) State the full and reduced model

b)Obtain SSE(F), SSE(R), df(F), fd(R), test statistics F for the general linear test and decision rule.

crime rate, high school grad %

  8487    74
   8179    82
   8362    81
   8220    81
   6246    87
   9100    66
   6561    68
   5873    81
   7993    74
   7932    82
   6491    75
   6816    82
   9639    78
   4595    84
   5037    82
   4427    79
   6226    78
  10768    73
   8335    77
  12311    65
  10104    77
  10503    76
   7562    79
   8593    79
   7133    78
  10205    84
  14016    78
   5959    81
   3764    89
   4297    85
   7562    77
   4844    74
   5777    80
   3599    84
   3219    88
  11187    75
   2105    77
   6650    78
  11371    61
   4517    91
   7348    83
   5696    77
   4995    85
   9248    70
   6860    88
   9776    80
   4280    82
  11154    82
   3442    82
   9674    70
   7309    64
   4530    79
   4017    83
   7122    77
   5689    76
   6109    80
   3343    84
   5029    82
   4330    81
   5425    74
   8769    81
   6880    76
   6538    78
   6521    78
   9423    79
   9697    83
   3805    79
   3134    83
   3433    81
   2979    84
   6836    64
   5804    67
   7986    75
  10994    73
  11322    77
   8937    64
   8807    75
  11087    80
  10355    83
   7858    85
   3632    91
   8040    88
   6981    83
   7582    76

When 41 people are used the Weight Watchers diet for one year, their weight losses had a standard deviation of 4.9lb. Use a 0.01 significance level to test the claim that the amounts of weight loss have a standard deviation equal to 6.0lb, which appears to be the standard deviation for the amounts of weight loss with the Zone diet. Write your assumptions before you conduct hypothesis testing.

Below you have a payoff table for a set of decisions that are under consideration.

                                               States of Nature

Alternative                  Low          High

Option A                     10              15

Option B                     12              13

Option C                     13               10

Choose the correspondence equation line for option A, B, and C:

Y= -5x+15x

Y=3x+10

Y=-X+13

In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.9 hours.

(a) The sample standard deviation was not reported, but suppose that it was 6 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.7 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

a. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

b. Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.     

c. Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

d. Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(b) Now suppose that the sample standard deviation was 2 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.7 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

a. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

b. Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.    

c. Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

d. Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(c) Explain why the hypothesis tests resulted in different conclusions for part (a) and part (b).

a.The larger standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 2.

b. The smaller standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 2, but not when the sample standard deviation is 6.     

c. The smaller standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 2.

d. The larger standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 2, but not when the sample standard deviation is 6.

1. A basketball player makes 54% of his shots during the regular season games.
a) To simulate whether a shot hits or misses you could assign random digits as
follows:
(i) One digit simulates one shot; 1 and 5 are a make, other digits are a miss.
(ii) One digit simulates one shot; odd digits are a make and even digits are a miss.
(iii) Two digits simulate one shot; 00 to 54 are a make and 55 to 99 are a miss.
(iv) Two digits simulate one shot; 00 to 53 are a make and 54 to 99 are a miss.
(v) Two digits simulate one shot; 01 to 54 are a make and 55 to 99 are a miss.

b) Using your choice in part (a) and these random digits below, simulate 10 shots.
12734 75390 20867 27513

c) Compute estimated probability:

Toyota’s marketing department is in the process of creating an ad meant to highlight the fuel efficiency of its Camry model compared to its Avalon model. Toyota knows that based on their production process, the miles per gallon (mpg) of both the Camry and the Avalon follow a normal distribution with the Camry having a standard deviation of 1.5 mpg and the Avalon having a standard deviation of 3.6 mpg. Toyota takes a sample of 50 Camry models and 60 Avalon models and finds that the Camry has a mean mpg of 31 while the Avalon has a mean mpg of 29.5 mpg. Toyota would like to know if there is sufficient evidence, at the alpha=0.01 level, to conclude that the Camry has a higher mpg than the Avalon. Answer the following questions.

1. What are the null and alternative hypotheses?

2. What is the critical value?

3. What is the test statistic?

4. What is the probability that you will find the Camry has a higher mpg but really it does not?

5. Will you reject or fail to reject the null hypothesis?

Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 39.2

inches and standard deviation of

1.9inches.

​a) What fraction of kindergarten kids should the company expect to be less than

33 inches​ tall?About blank ​% of kindergarten kids are expected to be less than 33 inches tall.

​(Round to one decimal place as​ needed.)

​b) In what height interval should the company expect to find the middle 80​% of​ kindergarteners?The middle 80​% of kindergarteners are expected to be between what inches and what inches.

​(Use ascending order. Round to one decimal place as​ needed.)

​c) At least how tall are the biggest 30​% of​ kindergarteners?The biggest 30​% of kindergarteners are expected to be at least ? inches tall.

​(Round to one decimal place as​ needed.)