You receive a brochure from a large university. The brochure indicates that the
ID: 3129848 • Letter: Y
Question
You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 3333 students. You want to test this claim. You randomly select 1818 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At alphaequals=0.050.05, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
37, 28, 32, 35, 32, 38, 23, 26, 28, 27, 33, 29, 25, 28, 29, 23
(a) Write the claim mathematically and identify Ho and Ha.
(b) Use technology to 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
a)
Claim: u < 33
This goes to the alternative hypothesis.
Formulating the null and alternative hypotheses,
Ho: u >= 33
Ha: u < 33 [HYPOTHESES]
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b)
As we can see, this is a left tailed test.
df = n - 1 = 15
Getting the test statistic, as
X = sample mean = 29.5625
uo = hypothesized mean = 33
n = sample size = 16
s = standard deviation = 4.574840617
Thus, t = (X - uo) * sqrt(n) / s = -3.005569189
Also, the p value is
p = 0.004435776 [ANSWER, P VALUE]
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c)
As P < 0.05, we REJECT THE NULL HYPOTHESIS. [ANSWER]
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d)
Hence, there is significant evidence at 0.05 level that the mean class size for full-time faculty is fewer than 33 students. [CONCLUSION]
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