The Next Questions Are Based On The Following Information:
A small community college claims that their average class size is equal to 35 students.This claim is being tested with a level of significance equal to 0.02 using the following sample of class sizes: 42,28,36,47,35,41,33,30,39,and 48.Assume class sizes are normally distributed.
-Which of the following conclusions can be drawn?
A)Since the test statistics equals 1.58,reject the null hypothesis and conclude that class size does not equal 35 students.
B)Since the test statistics equals 1.36,fail to reject the null hypothesis and conclude that there's insufficient evidence to conclude that class size does not equal 35 students.
C)Since the test statistics equals 2.05,reject the null hypothesis and conclude that class size does not equal 35 students.
D)Since the test statistics equals 2.26,fail to reject the null hypothesis and conclude that class size does equal 35 students.

Question

Quizplus · Accepted Answer

We need to perform a one-sample t-test to test the claim. The null hypothesis is that the mean class size is 35, and the alternative hypothesis is that it's not equal to 35. Since the sample size is small (less than 30) and the standard deviation of the population is unknown, we use the t-distribution with degrees of freedom n-1 = 9-1 = 8. We calculate the t-test statistic as (sample mean - hypothesized mean)/(sample standard deviation/sqrt(n)) = (363/10 - 35)/(6.88/sqrt(10)) = 1.36. This test statistic has a p-value of 0.101, which is greater than the level of significance of 0.02. Therefore, we fail to reject the null hypothesis and conclude that there's insufficient evidence to conclude that class size does not equal 35 students.

The Next Questions Are Based on the Following Information