Question 1041325: 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 aαequals=0.05, can you support the university's claim?
35 28 29 33 32 40 27 26 25 29 28 30 36 33 29 30 28 25
A. What is the P value?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Given Data Set
{35,28,29,33,32,40,27,26,25,29,28,30,36,33,29,30,28,25}
Using a calculator, we find that
sample mean = xbar = 30.16667
sample standard deviation = s = 4.00367
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)/(4.00367/sqrt(18))
t = -1.9427 5763 2601 19
t = -1.94
Now use a TI83 or TI84 calculator to compute the area to left of t = -1.94
Type in tcdf(-99,-1.94,17) to get the result 0.0344
So the p-value is approximately 0.0344
Side note: because the p value is smaller than alpha = 0.05, this means we reject the null hypothesis and conclude that the mean (mu) is smaller than 32
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