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 = 4.37.

(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 > 0.200

0.100 < p-value < 0.200    

0.050 < p-value < 0.100

0.025 < p-value < 0.050

0.010 < p-value < 0.025

p-value < 0.010

(c)

At

α = 0.05,

what is your conclusion?

Reject H₀. There is sufficient evidence to conclude that μ > 12.

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

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

Reject H₀. There is insufficient 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?

Reject H₀. There is sufficient evidence to conclude that μ > 12.

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

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

Reject H₀. There is insufficient evidence to conclude that μ > 12.

Answer 1

Solution :

Given that,

Population mean = = 12

Sample mean = = 14

Sample standard deviation = s = 4.37

Sample size = n = 25

Level of significance = = 0.05

This is a right - tailed test.

a)

The test statistics,

t = ( - )/ (s/)

= ( 14 - 12 ) / ( 4.37 /35)

= 2.708

b)

P- Value = 0.0053

p-value < 0.010

c)

= 0.05

The p-value is p =0.0053 < 0.05, it is concluded that the null hypothesis is rejected.

Reject H₀. There is sufficient evidence to conclude that μ > 12.

d)

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.691

Since it is observed that t = 2.708 = 1.691, it is then concluded that the null hypothesis is rejected.

Reject H₀. There is sufficient evidence to conclude that μ > 12.