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<p-value<0.025 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean class size of a middle school class within the district is less than 20 students? Select all that apply: A) Reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students. B) Fail to reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students. C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean class size of a middle school class within the district is less than 20 students. D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean class size of a middle school class within the district is less than 20 students.
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<p-value<0.025 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean class size of a middle school class within the district is less than 20 students?
Select all that apply:
A) Reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students.
B) Fail to reject the null hypothesis that the true population mean class size of a middle school class within the district is equal to 20 students.
C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean class size of a middle school class within the district is less than 20 students.
D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean class size of a middle school class within the district is less than 20 students.
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