Question

The dean of a university estimates that the mean number of classroom hours per week for​ full-time faculty is

11.011.0.

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

alphaαequals=0.100.10​,

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

10.810.8

9.49.4

12.712.7

6.16.1

4.94.9

10.110.1

13.213.2

8.88.8

​(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

Which of the following correctly states

Upper H 0H0

and

Upper H Subscript aHa​?

A.

Upper H 0H0​:

muμgreater than or equals≥11.011.0

Upper H Subscript aHa​:

muμless than<11.011.0

B.

Upper H 0H0​:

muμless than<11.011.0

Upper H Subscript aHa​:

muμgreater than or equals≥11.011.0

C.

Upper H 0H0​:

muμless than or equals≤11.011.0

Upper H Subscript aHa​:

muμgreater than>11.011.0

D.

Upper H 0H0​:

muμgreater than>11.011.0

Upper H Subscript aHa​:

muμless than or equals≤11.011.0

E.

Upper H 0H0​:

muμnot equals≠11.011.0

Upper H Subscript aHa​:

muμequals=11.011.0

F.

Upper H 0H0​:

muμequals=11.011.0

Upper H Subscript aHa​:

muμnot equals≠11.011.0

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

Pequals=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.

RejectReject

Upper H 0H0

because the​ P-value is

less thanless than

the significance level.

B.

RejectReject

Upper H 0H0

because the​ P-value is

greater thangreater than

the significance level.

C.

Fail to rejectFail to reject

Upper H 0H0

because the​ P-value is

greater thangreater than

the significance level.

D.

Fail to rejectFail to reject

Upper H 0H0

because the​ P-value is

less thanless than

the significance level.

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

A.At the

10​%

level of​ significance, there

is not is not

sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is

less thanless than

11.011.0.

B.At the

1010​%

level of​ significance, there

isis

sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is

11.011.0.

C.At the

1010​%

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 thangreater than

11.011.0.

D.At the

1010​%

level of​ significance, there

is notis not

sufficient evidence to reject the claim that the mean number of classroom hours per week for​ full-time faculty is

11.011.0.

Click to select your answer(s).

Answer 1

a)

H0: $\mu$ = 11

Ha: $\mu$$\neq$ 11

b)

From the given data,

Sample mean $\bar{x}$​​​​​​ = 9.5 , Sample standard deviation S = 2.9081

Test statistics

t = $\bar{x}$ - $\mu$ / S / sqrt(n)

= 9.5 - 11 / 2.9081 / sqrt(8)

= 1.46

This is test statistics value.

c)

Critical values at 0.10 level with 7 df = -1.895, 1.895

Since test statistics falls in non-rejection region, we fail to reject null hypothesis.

d)

At 10% 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