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 alphaequals0.05​, can you reject the​ dean's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed. 11.2 9.8 13.2 8.1 5.4 9.5 14.5 9.6 ​

(a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript a.

Which of the following correctly states Upper H 0 and Upper H Subscript a​? A.

Upper H 0​: muequals11.0 Upper H Subscript a​: munot equals11.0

B. Upper H 0​: muless than or equals11.0 Upper H Subscript a​: mugreater than11.0

C. Upper H 0​: mugreater than or equals11.0 Upper H Subscript a​: muless than11.0

D. Upper H 0​: mugreater than11.0 Upper H Subscript a​: muless than or equals11.0

E. Upper H 0​: munot equals11.0 Upper H Subscript a​: muequals11.0

F. Upper H 0​: muless than11.0 Upper H Subscript a​: mugreater than or equals11.0 ​

(b) Use technology to find the​ P-value.

Pequals =  ​(Round to three decimal places as​ needed.) ​

(c) Decide whether to reject or fail to reject the null hypothesis.

Which of the following is​ correct?

A. Fail to reject Upper H 0 because the​ P-value is less than the significance level.

B. Reject Upper H 0 because the​ P-value is greater than the significance level.

C. Reject Upper H 0 because the​ P-value is less than the significance level.

D. Fail to reject Upper H 0 because the​ P-value is greater than the significance level.

​(d) Interpret the decision in the context of the original claim.

A. At the 5​% level of​ significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is greater than 11.0.

B. At the 5​% level of​ significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is 11.0.

C. At the 5​% level of​ significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is less than 11.0.

D. At the 5​% level of​ significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is 11.0. Click to select your answer(s).

Answer 1

a. Here claim is that mean is 11

So hypothesis is

A. vs

b. Sample mean is

Create the following table.

data	data-mean	(data - mean)2
11.2	1.0375	1.07640625
9.8	-0.3625	0.13140625
13.2	3.0375	9.22640625
8.1	-2.0625	4.25390625
5.4	-4.7625	22.68140625
9.5	-0.6625	0.43890625
14.5	4.3375	18.81390625
9.6	-0.5625	0.31640625

Find the sum of numbers in the last column to get.

So standard deviation is

So test statistics is

Hence P value is TDIST(0.83,7,2)=0.4339

c. As P value is greater than alpha=0.05, we fail to reject the null hypothesis

Correct answer is

D. Fail to reject Upper H 0 because the​ P-value is greater than the significance level.

d. Hence we have sufficient evidence to support the claim that mean is 11

So answer here is D. At the 5​% level of​ significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is 11.0.