Answer the following questions showing all work. If you use Minitab Express include the appropriate output (copy + paste) along with an explanation. Output without explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

1. For each of the following, compute the correct degrees of freedom and find the correct t multiplier for constructing a confidence interval for a population mean using Minitab Express. [20 points]

A. Confidence level 85%, , df = _____, t* = ______

B. Confidence level 85%, , df = _____, t* = ______

C. Confidence level 95%, , df = _____, t* = ______

D. Confidence level 95%, , df = _____, t* = ______

E. How does the t multiplier change as the confidence level changes?

F. How does the t multiplier change as the sample size changes?

2. For the following scenarios, if you were to construct a confidence interval, what would be the appropriate multiplier? (State whether z* or t* AND look up the number) [20 points]

A. You want to estimate the proportion of Penn State students who own a Mac with 95% confidence. You take a simple random sample of 30 Penn State students.

B. You want to estimate the average weight of female Maine Coon cats with 95% confidence. You have a sample of 16 female Maine Coons.

C. You want to construct a 99% confidence interval for the mean number of credits completed by students enrolled in STAT 200 this semester across all campuses. You take a random sample of 850 students.

D. You want to construct a 90% confidence interval for the proportion of registered Pennsylvanian voters who plan to vote for Candidate A. You take a random sample of 50 registered voters in Pennsylvania.

E. You want to construct a 90% confidence interval for the average height of all Penn State World Campus students. You have a random sample of 27 World Campus students.

3. During the first week of class data were collected from a sample of World Campus STAT 200 students. This data can be found in the file SUMMER16STDATA.MTW. Use this data to answer the following questions. Copy + paste all relevant Minitab Express output. Clearly identify your answers. [60 points]

A. What proportion of students in this sample said that they own wearable technology (e.g., FitBit, Nike+, Jawbone)?

B. Compute a 95% confidence interval for the proportion of the population of all World Campus STAT 200 students who own wearable technology. Use the normal approximation method.

C. Interpret the confidence interval that you constructed in part B.

D. Is there evidence that the proportion of all World Campus STAT 200 students who own wearable technology is different from 50%? Explain why.

E. In this sample, what were the mean and standard deviation for the variable of height in inches?

F. Compute a 90% confidence interval for the mean height in inches in the population of all World Campus STAT 200 students.

G. Interpret the confidence interval that you constructed in part F.

H. Compute a 99% confidence interval for the mean height in inches in the population of all World Campus STAT 200 students.

I. Which is wider, the 90% confidence interval in part F or the 99% confidence interval in part H? Explain why.

J. If you wanted to construct a 95% confidence interval for the proportion of the population of all World Campus students who own wearable technology with a margin of error of 5%, what sample size should you obtain?

K. If you wanted to construct a 95% confidence interval for the proportion of the population of all World Campus students who own wearable technology with a margin of error of 1%, what sample size should you obtain?

L. Compare your results from parts J and K. Which is larger? Explain why.

M. If you wanted to construct a 95% confidence interval for the average height of World Campus students with a margin of error of 4 inches, what sample size should you obtain?