Statistics Review for Final Exam (2nd set)
(Chapter 6, 7, and 8)

1. In a New York modeling agency, a researcher wishes to see if the average height of female models is really less than 67 inches, as the chief claims. A sample of 30 models has an average height of 66.8 inches. The standard deviation of the population is 1.7 inches. At = 0.05, is the average height of the models really less than 67 inches? Use the P-value method.

2.  A magazine article stated that the average age of women who are getting married for the first time is 26 years. A researcher decided to test this hypothesis at =0.01. She selected a sample of 25 women who were recently married for the first time and found the average was 25.1 years. The population standard deviation was 3 years. Should the null hypothesis be rejected?

3. Membership in an elite organization requires a test score in the upper 30% range. If the variable is normally distributed with = 115 and = 12, find the lowest acceptable score that would enable a candidate to apply for membership.

4. A researcher wishes to estimate within $300 the true average amount of money a county spends on road repairs projects each year. If she wants to be 90% confident, how large a sample is necessary? The population standard deviation is known to be $900.

5. For a certain urban area, in a sample of 5 months, an average of 28 mail carriers were bitten by dogs each month. The standard deviation of the sample was 3. Find the 90% confidence interval of the true mean.

6. A random sample of 49 shoppers showed that they spend an average of $23.45 per visit at the Saturday Mornings Bookstore. The standard deviation of the population was $2.80. Find a point estimate of the population mean. Find the 90% confidence interval of the true mean.

7. The average repair cost of a microwave oven is $55, with a standard deviation of $8. The costs are normally distributed. If 12 ovens are repaired, find the probability that the mean of the repair bills will be greater than $60.

8. The average salary for graduates entering the business field is $40,000. If the salaries are normally distributed with a standard deviation of $5000, find the probability that

 a. An individual graduate will have a salary over $45,000.

 b. A group of 9 graduates will have a group average over $45,000.

9. 9. Drivers of a taxi company have an average of 12.4 years’ experience. In a study of 15 taxi drivers, the average experience was 11.2 years and the samples standard deviation was 2. At =0.10, test the claim that the number of years’ experience of the taxi drivers is less than 12.4 years.