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

11.011.0.

Click to select your answer(s).

Answer #1

a)

H0: = 11

Ha: 11

b)

From the given data,

Sample mean = 9.5 , Sample standard deviation S = 2.9081

Test statistics

t = - / 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

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