Exam 11: Inference on Two Samples

Determine the Appropriate Hypothesis Test to Perform -The table below shows the weights, in pounds, of seven subjects before and after following a particular diet program for three months. Does the sample evidence suggest that the diet program is effective in reducing weight? Use the $\alpha = 0.01$ level of significance. Assume that the differenced data come from a population that is normally distributed with no outliers. Subject A B C D E F G Before, 183 160 193 184 188 151 185 After, 176 151 191 189 174 153 173

Provide an appropriate response. -Find the standardized test statistic, $\mathrm { z }$ to test the hypothesis that $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ . Use $\alpha = 0.05$ . The sample statistics listed below are from independent samples. Sample statistics: $\mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 1 } = 35$ , and $\mathrm { n } _ { 2 } = 60 , \mathrm { x } _ { 2 } = 40$

Use McNemar s Test to Compare Two Proportions from Matched -pairs Data -Two surgical procedures are widely used to treat a certain type of cancer. To compare the success rates of the two procedures, random samples of the two types of surgical patients were obtained and the numbers of patients who showed no recurrence of the disease after a 1-year period were recorded. The data are shown in the table. How large a sample would be necessary in order to estimate the difference in the true success rates to within $0.10$ with $95 \%$ reliability? Number of Successes Procedure A 100 95 Procedure B 100 83

Test Hypotheses Regarding the Difference of Two Independent Means -A study was conducted to determine if the salaries of librarians from two neighboring states were equal. A sample of 100 librarians from each state was randomly selected. The mean from the first state was $29,300 with a standard deviation of $2300. The mean from the second state was $30,700 with a standard deviation of $2100. Test the hypothesis that the salaries from both states are equal. Use = 0.05.

Determine the Appropriate Hypothesis Test to Perform -In a survey, 64 of 133 women said that they regularly remember their dreams, while 60 of 128 men said that they regularly remember their dreams. Does this constitute sufficient evidence to conclude that women are more likely to remember their dreams than men? Use the $\alpha = 0.05$ level of significance.