You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18...

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At α = 0.01, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

32 27 32 34 30 37 24 25 29 30 27 33 33 32 27 29 25 23

(a) Write the claim mathematically and identify H₀
and H_a

(b) Use technology to find the P-value.

P = ___________ (Round to three decimal places as needed.)

(c) Decide whether to reject or fail to reject the null hypothesis.


Which of the following is correct?

A. Reject H₀
because the P-value is greater than the significance level.

B. Fail to reject H₀ because the P-value is less than the significance level.

C. Reject H₀
because the P-value is less than the significance level.

D. Fail to reject H₀
because the P-value is greater than the significance level.

(d) Interpret the decision in the context of the original claim.

A. At the 1% level of significance, there is sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 31students.

B. At the 1% level of significance, there is sufficient evidence to support the claim that the mean class size for full-time faculty is more than 31 students.

C. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 31 students.


D. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is more than 31 students.