Question

The dean of a University estimates that the mean number of classroom hours for full time faculty is 11.0. As a member of sydent council, you want to test the claim. A sample of the number of classroom hours for 8 full-time faculty is shown below.

                 11.8 6.4 8.6 10.4 12.6 13.6 7.9 9.1

At the .01 level of significance, is the Dean’s claim valid? Use the P-value approach. Clearly state the null and alternative hypotheses. Locate the claim and state the decision.

Answer 1

Solution:

x	x2
11.8	139.24
6.4	40.96
8.6	73.96
10.4	108.16
12.6	158.76
13.6	184.96
7.9	62.41
9.1	82.81
∑x=80.4	∑x2=851.26

Mean ˉx=∑xn

=11.8+6.4+8.6+10.4+12.6+13.6+7.9+9.1/8

=80.4/8

=10.05

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√851.26-(80.4)28/7

=√851.26-808.02/7

=√43.247

=√6.1771

=2.4854

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 11.0

Ha :     11.0

Test statistic = t

= ( - ) / s / n

= (10.05-11.0) / 2.48 / 8

= −1.083

Test statistic = t = −1.083

P-value =0.3145

= 0.01  

P-value >

0.3145 > 0.01

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that