Confidence Interval & Hypothesis Testing

1. In each of the following exercises, a set of condition is given. To construct a 95 percent confidence interval for the population mean, would you use the z distribution, a t distribution, or neither? Where appropriate, determine the z or t value.
n = 21, xbar = 23.1, s = 7.5, population distribution shape normal, σ = 7.9.

2. The same issue of the American Journal of Psychiatry reported that an IQ test was administered to a random sample of 26 chronic schizophrenic patients and the mean was found to be 97.6. For this test, the population values are known as to be normally distributed with a standard deviation of 15. Construct a 90 percent confidence interval for the mean IQ of the population of chronic schizophrenic patients.

3. A study in the American Journal of Psychiatry has found that of a random sample of 63 World War II POW survivors, 24 reported they had recurrent distressing dreams. Form a 90 percent confidence interval for the population percentage of such POW survivors who have recurrent distressing dreams.

4. For each of the following, use the seven-step classical hypothesis-testing procedure (and where necessary, assume the population is normally distributed):
Test the claim that µ is equal to 50 at the .05 level of significance. Use sample data of n = 45, xbar = 48.3, σ = 5.1.

5. According to Management Accounting salary figures fir certified management accountants (CMAs) who are in the field less than 1 year are randomly distributed with a mean of $31,129. A random sample of 15 first-year CMAs in Denver produces a mean salary of $32,379, with a standard deviation of $1,797. Test the hypothesis that the mean for all Denver first-year CMAs is not equal to$31,129. Use the .05 level of significance.

6. It is widely thought that there is a high incidence of disability among the homeless population. The Transbay Outreach staff in the San Francisco area surveyed a random sample of 87 homeless people not living in shelters and found that 67 were disabled in one or more categories (such as substance abuse, psychiatric disability, or medical disability). Test the hypothesis that over 75 percent of all the homeless people in the San Francisco area not living in shelters have one or more types of disability. Use the .01 level of confidence.

7. It was reported in the 1990 National Health Interview Survey that 28.4 percent of all men in the United States smoked cigarettes. A later study conducted to determine the smoking habits of physicians was reported in the American Journal of Public Health. From a random sample of 337 male physicians, 34 reported that they are current smokers. Test the hypothesis at the .01 level that the percent of all male physicians who are smokers is less than 28.4.