# Statistics Exam

Instructions: Answer the following four questions. Write legibly and show all work. Begin each numbered question on a fresh page. Unsupported answers will receive zero points. You must work independently.

Due: Monday 6/

1

8, 11:

5

9pm

1. Consider the following five bundles of pens containing the quantities shown below.

30

 Bundle Number of Pencils (Population) 1 3 0 2 18 3 4 33 5 36

(a) How many different samples of two bundles each are there?

(b) List all possible samples of size two and compute the mean of each sample.

(c) Calculate the population mean and compare it to the mean of the sampling distribution.

2. A research was conducted at WPU to find the average amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The research showed that the student population studied an average of 20 hours per week with a standard deviation of 10 hours.

(a) What is the standard error of the mean?

(b) What is the probability that a sample mean would exceed 20 hours per week?

(c) What is the probability of finding a sample mean less than 18 hours?

(d) What is the probability that average student study time is between 18 and 22 hours?

3. A research study of an urban university, with population of 25,450, showed that 870 of 1100 students sampled attended a home basketball game during the season. What inferences can be made about student attendance at basketball games?

(a) What is the estimated proportion for the population?

(b) Using the 95% level of confidence, what is the confidence interval?

(c) Using the 99% level of confidence, what is the confidence interval?

4. A research study related to health and health costs, surveyed 30 families. It found that the annual health insurance premiums for a family with coverage through an employer averaged \$16,469. The standard deviation of the sample was \$2,000.

(a) What is the population mean? What is the best estimate of the population mean?

(b) Based on this sample information, develop a 95% confidence interval for the population mean yearly premium.

(c) How large of a sample is needed to assess the population mean with an allowable error of \$600 at 99% confidence?

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