The dean of a university estimates that the mean number of classroom hours per w

Question

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a=0.01, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

Data: 12.8, 8.9, 13.5, 8.2, 6.5, 11.4, 12.2, 8.6

(a) Write the claim mathemathically 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) Interprete the decision in the context of the orginal claim

Explanation / Answer

Null hypothesis:

Ho = The mean classroom hours per week for full-time faculty is 11.

Ho = µ = 11

H1 = The mean classroom hours per week for full-time faculty is not 11.

H1 = µ 11

Using R language for testing the hypothesis:

> x<-c(12.8,8.9,13.5,8.2,6.5,11.4,12.2,8.6)

>t.test(x,conf.level=0.99,mu=11)

        One Sample t-test

data: x

t = -0.82273, df = 7, p-value = 0.4378

alternative hypothesis: true mean is not equal to 11

99 percent confidence interval:

7.125532     13.399468

sample estimates:

mean of x

10.2625

The p-value = 0.4378

p-value = 0.4378 > 0.01 =

We fail to reject the null hypothesis.

The claim of the dean of the university is correct. The mean classroom hours per week for full-time faculty is 11.

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