Question

Consider the following hypothesis test.

H₀: μ ≤ 12

H_a: μ > 12

A sample of 25 provided a sample mean

x = 14

and a sample standard deviation

s = 4.28.

(a)

Compute the value of the test statistic. (Round your answer to three decimal places.)

(b)

Use the t distribution table to compute a range for the p-value.

p-value > 0.2000.100 < p-value < 0.200    0.050 < p-value < 0.1000.025 < p-value < 0.0500.010 < p-value < 0.025p-value < 0.010

(c)

At

α = 0.05,

what is your conclusion?

Do not reject H₀. There is insufficient evidence to conclude that μ > 12.Reject H₀. There is sufficient evidence to conclude that μ > 12.    Reject H₀. There is insufficient evidence to conclude that μ > 12.Do not reject H₀. There is sufficient evidence to conclude that μ > 12.

(d)

What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer to three decimal places.)

test statistic≤test statistic≥

What is your conclusion?

Do not reject H₀. There is insufficient evidence to conclude that μ > 12.Reject H₀. There is sufficient evidence to conclude that μ > 12.    Reject H₀. There is insufficient evidence to conclude that μ > 12.Do not reject H₀. There is sufficient evidence to conclude that μ > 12.

Answer 1

Given:

= 12, sample mean () = 14, Sample standard deviation (S) = 4.28

Test statistic:

Degrees of Freedom = n - 1 = 25-1 = 24

b)

P-value = 0.0141

ANSWER: D

0.010 < P-value < 0.025

C)

At = 0.05

P-value < . i.e. 0.0141 < 0.05, That is Reject Ho at 5% level of significance.

ANSWER: B

Reject Ho. There is sufficient evidence to conclude that   > 12

d)

Rejection Rule:

Test statistic > Critical value, Then Reject Ho at 5% level of significance.

Critical value:

...............................From t distribution table

Here,

Test statistic > Critical value, i.e. 2.336 > 1.7109. That is Reject Ho at 5% level of significance.

ANSWER: B

Reject Ho. There is sufficient evidence to conclude that   > 12