NAME:

You may use additional sheets of paper to solve the following questions, but please report your results and conclusions in the space provided. Whenever possible, show your work for potential partial credit. NOTE: When performing numerical calculations, keep at least 4 digits after a decimal. (I.e., do NOT round .2265 to .23 or .227) BUDGET YOUR TIME WISELY!

1. What important roles do the population mean (m) and standard deviation (s) play in the normal distribution? Using diagrams, show how different values of both m and s will alter the curve. (10 points)

2. Internet Magazine monitors Internet service providers (ISPs) and provides statistics on their performance. The average time to download a web page for free ISPs is approximately 20 seconds for European web pages (Internet Magazine, January, 2000). Assume the time to download a web page follows an exponential distribution.

a. What is the probability it will take less than 10 seconds to download a web page? (3 points)

b. What is the probability it will take between 10 and 30 seconds to download a web page? (3 points)

3. Suppose I want to use a sample of college students to make predictions on the overall drinking habits (as measured by drinks per week) for the population of all college students in the U.S. In general, describe the sampling distribution for the mean # of drinks per week. Include the expected value and standard deviation. Describe the important role that the Central Limit Theorem plays here. Use diagrams where necessary. (15 points)

4. Suppose all college students sleep an average of 6.55 hours during the week (Sunday through Thursday) with a standard deviation of 1.02 hours. If you took a random sample of 192 college students from a population of 1050, what is the probability that you calculate a sample mean of 6.4 hours or more? (7 points)

5. Your nosy roommate, reading over your shoulder while you study, asks you to explain a 99% confidence interval and why we find it useful to construct them. Spend a little time explaining to her how confidence intervals relate to population parameters, sampling distributions and sampling error. Be thorough, she has had no exposure to the concepts. Feel free to use an example if that helps her understand. (15 points)

6. According to ORC International, 71% of Internet users connect their computers to the Internet by normal telephone lines (USA Today, January 18, 2000). Assume a population proportion of .71. What is the probability that the sample proportion for a simple random sample of 350 Internet users will be within plus or minus .05 of the population proportion? (7 points)

7. A national magazine reports that a random sample of 190 U.S. college students rate their “quality of life” as an average of 7.1626; where 10 is the highest. The sample standard deviation is 1.4546. Construct a 99% confidence interval estimate for the population mean ranking of “quality of life”. Explain what your interval tells you. If you were the President of a college, would you be concerned? Why? (12 points)

8. Suppose that a national study of college alumni says that a good indicator of whether alumni donate money back to their alma mater is the proportion of alumni who would attend the college again, if given the chance. If this proportion is below .75, the college should be concerned about future donations and alumni support. You have surveyed 188 current Hanover College students and in response to the question: “Knowing what you know now, and if you were a senior in high school, would you choose Hanover again?” the sample proportion that said “yes” was .7287. Develop a hypothesis test to determine whether Hanover College should be concerned about future donations. Explain why you set it up the way that you did, choose an appropriate level of significance and clearly explain the results of your test and what it means to an administrator whose job it is to contact alumni for donations. (18 points)

9. What is a p-value and how is it used to conduct a hypothesis test? Use the test from #8 above as a good illustration. (10 points)