You receive a brochure from a large university. The brochure indicates that the

Question

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 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 =0.01, can you support the university's claim? 36 25 27 35 35 42 27 27 27 27 32 35 32 31 29 27 27 22 (a) Write the claim mathematically and identify H0 and Ha. (b) Find the P-value. (c)Decide whether to reject or fail to reject the null hypothesis. (d) Interpret the decision in the context of the original claim.

Explanation / Answer

Given Data Set
{36 25 27 35 35 42 27 27 27 27 32 35 32 31 29 27 27 22}
Using a calculator, we find that
sample mean = xbar = 30.166666666666668  =30.17
sample standard deviation = s = 4.949747468305832  =4.9497


Hypothesis
H0: mu >= 32
H1: mu < 32
This is a one-tailed test. Specifically a left-tailed test.

Test statistic:
t = (xbar - mu)/(s/sqrt(n))
t = (30.16667 - 32)/(4.9497/sqrt(18))
t = -1.571440784
t = -1.57144

Now use a TI83 or TI84 calculator to compute the area to left of t = -1.57144

The P-Value is 0.067304

Side note: because the p value is greater than alpha = 0.01, this means we failed reject the null hypothesis and conclude that the mean (mu) is not smaller than 32

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