Applied Regression Modeling. Iain Pardoe

average number of classes missed per student during a quarter is 2. College professors dispute this claim and believe that the average is more than this. They sample students and find that the sample mean is 2.3 and the sample standard deviation is 0.6. State the null and alternative hypotheses that the professors wish to test. Then calculate the test statistic for this test and, using a 5% significance level, determine who appears to be correct, the students or the professors. (You may find some of the following information useful: The 95th percentile of the t‐distribution with 15 degrees of freedom is 1.753; the 97.5th percentile of the t‐distribution with 15 degrees of freedom is 2.131.)Consider the following computer output:Sample size, 150Mean2.94Standard deviation0.50Suppose that we desire a two‐tail test of the null hypothesis that the population mean is equal to 3 versus the alternative hypothesis that the population mean is not equal to 3. Find upper and lower limits for the p‐value for the test. (You may find some of the following information useful: The 90th percentile of the t‐distribution with 149 degrees of freedom is 1.287; the 95th percentile of the t‐distribution with 149 degrees of freedom is 1.655.)A developer would like to see if the average sale price of condominiums in a particular locality has changed in the last 12 months. A study conducted 12 months ago indicated that the average sale price of condominiums in this locality was $. Data on recent sales were as follows:Sample size, 28MeanStandard deviationWrite down the null and alternative hypotheses for this problem. Then specify the rejection region for conducting a two‐tail test at significance level 5%. Based on the computer output, would you reject or fail to reject the null hypothesis for this test? (You may find some of the following information useful: The 95th percentile of the t‐distribution with 27 degrees of freedom is 1.703; the 97.5th percentile of the t‐distribution with 27 degrees of freedom is 2.052.)In a hypothesis test, is it true that the smaller the p‐value, the less likely you are to reject the null hypothesis? Explain.