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

α=0.05​,

can you reject the​ dean's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.

12.3

7.2

11.8

7.5

6.8

9.1

13.2

9.1

​(a) Write the claim mathematically and identify

H0

and

Ha.

Which of the following correctly states

H0

and

Ha​?

A.

H0​:

μ≤11.0

Ha​:

μ>11.0

B.

H0​:

μ=11.0

Ha​:

μ≠11.0

C.

H0​:

μ>11.0

Ha​:

μ≤11.0

D.

H0​:

μ≥11.0

Ha​:

μ<11.0

E.

H0​:

μ≠11.0

Ha​:

μ=11.0

F.

H0​:

μ<11.0

Ha​:

μ≥11.0

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

P=nothing

​(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. Reject H0 because the​ P-value is greater than the significance level.

B. Fail to reject H0 because the​ P-value is less than the significance level.

C. Reject H0 because the​ P-value is less than the significance level.

D. Fail to reject H0 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 not 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 sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is 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 less than 11.0.

Answer 1

∑x = 77

∑x² = 784.72

n = 8

Mean , x̅ = Ʃx/n = 77/8 = 9.625

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(784.72-(77)²/8)/(8-1)] = 2.4956

--

a) Null and Alternative hypothesis: Answer B.

Ho : µ = 11

H1 : µ ≠ 11

b)

Test statistic:

t = (x̅ - µ)/(s/√n) = (9.625 - 11)/(2.4956/√8) = -1.5584

df = n-1 = 7

p-value = T.DIST.2T(ABS(-1.5584), 7) = 0.163

c)

Decision:

D. Fail to reject H0 because the​ P-value is greater than the significance level.

d)

Conclusion:

B. 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.