Question

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. (NOTE: We need to assume that class sizes are normally distributed in order to use the t distribution because the sample size n=10 < 25, and the Central Limit Theorem does not apply.)

Which of the following conclusions can be drawn?

• A.

  Since the test statistic 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.

• B.

  Since the test statistic equals 2.26, fail to reject the null hypothesis and conclude that class size does equal 35 students.

• C.

  Since the test statistic equals 2.05, reject the null hypothesis and conclude that class size does not equal 35 students.

• D.

  Since the test statistic equals 1.58, reject the null hypothesis and conclude that class size does not equal 35 students.

Answer 1

Let denotes the average class size.

ans-> A) Since the test statistic 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.