The decline of cigarettes:  In the last 10 years, the Gallup poll has asked random sample of 1500 Americans:  "Have you, yourself, smoked any cigarettes in the past week?  The percentage answering "yes" fluctuated as follow:

1. Check and calculate the summary statistics  (mean, median, mode, sdv, min, max, Q1, Q3).  Please give a brief interpretation of each measure.
2. Please drawn in a graph to show how this percentage fluctuates over years?  Are they any outlier in your data?.  Drawn in your data without this outlier?
3. Calculate a 95% confidence interval for the population proportion who smoked in 1990.  Also for 1999.  Explain clearly and briefly what "95% confidence "means".

4)         Calculate a 95% confidence interval for the change in the population proportion who smoked between 1989 and 1994? Please give a brief interpretation of your result.

5)                 Calculate a 95% confidence interval for the change in the population proportion who smoked between 1990 and 1999? Please give a brief interpretation of your result.

6)                 Is this data good evidence that the proportion of people who smoke has declined over the past ten years?

7)         Discuss some of the main limitations of these data.

Women are filling managerial positions in increasing numbers, although whether they progress fast enough it still debated.  Does marriage hinder a woman’s career progression more than a man’s? A recent article (Stroh et al., 1992) investigated this and other questions relating to managerial careers of men and women in today’s work force in the health care sector.  In a random sample of 795 male managers and 223 female managers from 20 companies in the health sector, 86% of the male managers and 45% of the female managers were married.

1. Use a 95% confidence interval to estimate the difference between the proportion of men and women who are married?

2)                 Interpret the interval. Sate your conclusion in terms of the population from which the sample was drawn.

An auditor was hired to verify the accuracy of a hospital’s new billing system.  The auditor randomly sampled 35 invoices produced since the system was installed.  Each invoice was compared against the relevant internal records to determine by how much the invoice was in error.  The amount of the error X, was defined as (A-I), where A is the actual amount owed the company and I is the amount indicated in on the invoice.  The auditor found that the mean of x = $ 1 and standard deviation was $124.

1. Identify the population the auditor studied
2. Describe the variable that the auditor measured
3. Construct a 98% confidence interval for the mean error per invoice.
4. Interpret the confidence interval
5. Comment on the accuracy of the billing system
   Pharmaceutical companies spend millions of dollars annually on research and development of new drugs to benefit society.  After a new drug is formulated, the pharmaceutical company must subject it to lengthy and involved testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug.  The pharmaceutical company must provide substantial evidence that a new drug is safe prior to receiving FDA approval, so that the FDA can confidently certify the safety of the drug.
   1. If the new drug testing were to be placed in a test-of-hypothesis framework, would the null hypothesis be that the drug is safe or unsafe? The alternative hypothesis?
   2. Given the choice of null and alternative hypotheses in part a, describe Type I and Type II errors in terms of this application.  Define \(\alpha \) and \(\beta \) of this application.
   3. If the FDA wants to be very confident that the drug is safe before permitting it to be marketed, is it more important that \(\alpha \) or \(\beta \) be small? Explain.

1)                 Set up a 90% confidence interval estimate of the population average waiting time?

2)                 Test the null hypothesis at 10% significant level that waiting time is not greater than 20 minutes?

3)         Suppose that the value of 1.9 minutes was actually 101.9 minutes.  What would be your answer to (a).  What effect does this change have on your confidence interval and test?

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