Problem 1

For each of the following values of , and n, find t/2,n1. Round the answer to two digits after the decimal point.

(a) = 0.10, n = 25.

(b) = 0.02, n = 10.

. . . . . . . . .

Problem 2

Consider the time it takes for a call center to answer its calls. A random sample of 7 calls revealed a sample mean time of 191 seconds and a sample standard deviation of 11.4 seconds.

1. What is the sample?
2. What is the population?
3. Explain what the population mean represents in this problem.
4. Construct a 95% confidence interval for the population mean.
5. Construct a 99% confidence interval for the population mean.

(f) State any assumptions you needed for this problem. Do you think that the assumptions are reasonable? Why or why not?

. . . . . . . . .

Problem 3

Consider (again) the time it takes for a call center to answer its calls. Assume the time to answer a call is normally distributed. The call center claims that the mean time to answer a call is 3 minutes. In a random sample of 7 calls, the average time for the call center to answer was 191 seconds, with a sample standard deviation of 11.4 seconds.

(a) Provide the null and alternative hypotheses for testing the call center's claim.

1. Compute the test statistic.
2. Compute the p-value.

(d) Test the call center's claim, at the 1% level of significance.

. . . . . . . . .

Problem 4

You would like to estimate the proportion of Stern students who participates in course faculty evaluations (CFEs). If you want to construct a 95% confidence interval for this proportion, how many students should you survey to guarantee that the width of your confidence interval will be less than 0.05? Hint: use the fact that p(1 p) 1/4, for any p taking values between [0, 1].