Question

Members of the school committee for a large city claim that the population mean class size of a middle school class within the district is exactly 20 students. Karla, the superintendent of schools for the city, thinks the population mean is less. She selects a random sample of 35 middle school classes across the city. The sample mean is 18.5 students with a sample standard deviation of 3.7 students. The test statistic t for a hypothesis test of H0:μ=20 versus Ha:μ<20 is t≈−2.40. If 0.01

Answer 1

To perform a hypothesis test, compare the test statistic with the critical value or p-value. The critical value is t_alpha with n-1 degrees of freedom. If the test statistic falls outside of the critical region, we can reject the null hypothesis.

Step-by-step explanation:

To perform a hypothesis test, we need to compare the test statistic with the critical value or p-value. In this case, the test statistic is t = -2.40. The question states that the level of significance is 0.01, which means the critical value will be tα with n-1 degrees of freedom.

Since the alternative hypothesis is μ < 20, this is a one-tailed test. We need to find the critical value of tα using the t-distribution table with (n-1) degrees of freedom.

If the test statistic falls in the rejection region (outside of the critical region), we can reject the null hypothesis that the population mean is 20 and conclude that the population mean is less than 20. Otherwise, if the test statistic falls within the critical region, we fail to reject the null hypothesis.