Question 2

Consider a random variable T that has a t-dstribution with k - 13 degrees of freedom. What is P(T >-0.6)

0 0.6000

0 0.3821

0 0.4375

0 0.7206

0 0.2794

Question 34 pts

Consider a random variable T that has a t-distribution with k 12 degrees of freedom. What is the probability that T falls between O and 1.8, i.e., what is P(O < T < 1.8)?

0 0.5000

0 1.8000

0 0.6821

0 0.4515

0 0.9515

Question 44 pts

Consider a random variable T that has a t-distribution with k 7 degrees of freedom. What is the value t* such that the probability in the tail to the left of t* equals 0.01?

0 -1.3232

O 1.3232

O 2.9980

0 -2.9980

0 -1.7613

Question 5

4 pts

Consider a random variable T that has a t-distribution with k

O -1.3232

0 2.9980

0 1.7613

0 1.3232

O -1.7613

O -2.9980

14 degrees of freedom. What is the value t* such that the probability in the tail to the right of t* equals

Question 65 pts

A large city newspaper contains several hundred advertisements for one-bedroom apartments. You choose 39 at random and calculate a mean monthly rent of $890 and a standard deviation of $103.

What is the standard error of the mean?

Round your answer to one decimal place of accuracy.

Question 74 pts

A large city newspaper contains several hundred advertisements for one-bedroom apartments. You choose 30 at random and calculate a mean monthly rent of $1234 and a standard deviation of $107.

What are the degrees of freedom for a standardized sample mean with a one-sample t statistic?

Question 87 pts

Consider an SRS of size 100 of cell phone users in which they are asked how many minutes per day they use their cell phones. The sample mean is 127.0 minutes. The sample standard deviation is 23.9 minutes.

Calculate the lower endpoint of a 95% confidence interval for the population mean (number of minutes using the cell phone.

C) 131.7 minutes

C) 117.9 minutes

C) 122.3 minutes

C) 123.7 minutes

C) 108.6 minutes

Question 9

For the historical period 1926-2015, here are the sample statistics for the inflation-adjusted total returns on investnnent grade corporate bonds:

sample size: n = 90

- 3.38%

s - 9.50%

Construct the one-sample t-confidence interval for a 0.99 level confidence interval for the population mean return.

O (0.00%, 9.90%)

O (1.72%, 5.04%)

O (-6.12%, 12.88%)

O (0.74%, 6.02%)

Question 107 pts

A manufacturer of industrial bolts for riding mowers requires that a particular type of bolt be 12.0 mm. in diameter. Periodically, the company draws an SRS of 30 bolts from recent batches and measures them to determine whether the manufacturing process is producing the desired diameter. The null hypothesis is Ho: g = 12.0. The alternative hypothesis is HA: 12.0.

In the most recent sample, the mean diameter was 11.91 mm. and the sample standard deviation was 0.11 mm.

What is the value of the one-sample t-statistic?

Round your answer to 2 decimal places of accuracy.

Question 117 pts

A manufacturer of industrial bolts for riding mowers requires that a particular type of bolt be 8.00 mm. in diameter. Periodically, the company draws an SRS of 30 bolts from recent batches and measures them to determine whether the manufacturing process is producing the desired diameter. The null hypothesis is Ho: g = 8.00. The alternative hypothesis is HA: 8.00.

In the most recent sample, the mean diameter was 7.95 mm. and the sample standard deviation was 0.10 mm.

What is the P-value for the hypothesis test (to four decimal places of accuracy)?

0 0.0052

0 0.0792

0 0.0104

0 0.0500

0 0.1000

Question 127 pts

Consider the 2016 rental listings for Manhattan in New York City for non-doorman one bedroom apartments. Suppose that the mean monthly rental for 2016 is $3,500. Suppose that you are interested in whether rental rates for this type of apartment are changing. Your null hypothesis is Ho: $3,500 per month versus HA: $3,500 per month.

You conduct an SRS of size 40 ads in February for this type of apartment in Manhattan. Your sample statistics:

- $3,575

s - $727

What is the P-value for the hypothesis test (to four decimal places of accuracy)?

0 0.3763

0 0.2590

0 0.5179

0 0.1078

0 0.4211

Question 137 pts

Suppose that you have been following the investment advice of your broker. Annual returns on diversified portfolios tend to be close to a Normal distribution. The mean annual total return on an S&P 500 index mutual fund has historically been about 11.95%. However, you suspect that your broker has been giving you bad advice and that your portfolio returns are lower.

Your null hypothesis is Ho: 11.95% per year versus HA: < 11.95% per year.

Your sample statistics for your most recent 20 years of returns:

6.31%

s - 21.35%

(Assume that this data approximates a simple random sample.)

What is the P-value for the hypothesis test (to four decimal places of accuracy)?

0 0.0500

0 0.1260

0 0.3171

0 0.2520

0 0.0630

Kaplan offers test preparation for taking the SAT. To determine whether their current program truly helps students do better on the SAT exam, they hire an outside auditor to evaluate the program. The auditor selects an SRS of senior high school students who have not yet taken the SAT. Each student takes the SAT, and the auditor records their scores; these are the pretest scores. Then each student participates in the Kaplan SAT preparation program. After completing the program, each student takes the SAT a second time, and the auditor records their scores; these are the posttest scores.

The variable X for each subject equals the posttest score minus the pretest score. X is positive if the subject improved his or her SAT score. The population mean for X is

The null hypothesis is no change in SAT score: Ho: 0. Kaplan is only interested in whether the training improves the score. Hence, the alternative hypothesis is HA:

Description of the sample:

The sample size is n 300 subjects

The sample mean change is score is 12

The sample standard deviation is s 180

What is the P-value for the one-sided one-sample t-test?

0 0.1246

0 0.0500

0 0.0180

0 0.0875

0 0.0360

Question 155 pts

A manufacturer of industrial bolts for riding mowers requires that a particular type of bolt be 8.00 mm. in diameter. Periodically, the company draws an SRS of 30 bolts from recent batches and measures them to determine whether the manufacturing process is producing the desired diameter. The null hypothesis is Ho: g = 8.00. The alternative hypothesis is HA: 8.00.

Based on the most recent sample, the t-statistic is 1.9562 and the corresponding P-value is 0.0601. Which of the following is the correct formal summary of the results?

O df -30, P = 0.0601

0 t = 1.9562, df- 29, P = 0.0601

The U.S. Department of Agriculture (USDA) uses sample surveys to estimate nationwide crop prices. Suppose that the USDA draws an SRS of corn producers in March and then a second, independent SRS of corn producers in September. In each survey, the USDA collects sales price per bushel of corn for each producer.

Summary statistics (prices per bushel)

Population

Sample size

Sample standard

Sample mean deviation

#1: corn prices,

March

50

$3.82$0.28

#2: corn prices, Sept.

62

$3.49$0.34

Calculate the lower endpoint of the 99% confidence interval for the difference in population mean corn prices, "2. Use the simple method to estimate the number of degrees of freedom.

O $0.49

O $0.28

O $0.21

O $0.37

O $0.18

Question 177 pts

The U.S. Department of Agriculture (USDA) uses sample surveys to estimate nationwide crop prices. Suppose that the USDA draws an SRS of corn producers in March and then a second, independent SRS of corn producers in September. In each survey, the USDA collects sales price per bushel of corn for each producer.

Summary statistics (prices per bushel)

Sample standard

PopulationSample size Sample mean

deviation

#1: corn prices,

50$3.82$0.28

March

#2: corn prices,

62$3.49$0.34

Sept.

Calculate the upper endpoint of the 99% confidence interval for the difference in population mean corn prices, "2. Use the simple method to estimate the number of degrees of freedom.

O $0.48

O $0.21

O $0.37

O $0.18

O $0.28

Question 187 pts

Suppose that you run a two-sample study to compare two sets of instructions on how to assemble a new machine. You randomly assign each employee to one of the instructions and measure the time (in minutes) it takes to assemble. Here is the data:

Sample standard

PopulationSample size Sample mean

deviation

Instruction set #1 2012012

Instruction set #2 201108

The null hypothesis is Ho: "1 = 112. The alternative hypothesis is Ho: PI 11.2. Calculate the two-sample t-statistic. (Use the simple method to estimate degrees of freedom k.)

0 3.10

0 2.63

0 2.98

0 2.25

0 3.42

Question 197 pts

Suppose that you run a two-sample study to compare two sets of instructions on how to assemble a new machine. You randomly assign each employee to one of the instructions and measure the time (in minutes) it takes to assemble. Here is the data:

Sample standard

PopulationSample size Sample mean

deviation

Instruction set #1 25

Instruction set #2 20

The null hypothesis is Ho:

0 0.0923

0 0.0377

0 0.0167

0 0.0412

0 0.0245

12713

11810

= 112. The alternative hypothesis is Ho: PI #12. Calculate the P-value. (Use the simple method to estimate degrees of freedom k.)