Question

In: Statistics and Probability

Consider the following hypothesis test. H0: μ ≤ 12 Ha: μ > 12 A sample of...

Consider the following hypothesis test.

H0: μ ≤ 12

Ha: μ > 12

A sample of 25 provided a sample mean

x = 14

and a sample standard deviation

s = 4.57.

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

Solutions

Expert Solution

Solution :

= 12

= 14

s = 4.57

n = 25

df = n-1 = 25-1 = 24

This is the right tailed test .

The null and alternative hypothesis is

H0 :   ≤ 12

Ha : > 12

a) Test statistic = t

= ( - ) / s / n

= (14-12) / 4.57 / 25

= 2.188

b) p(Z >2.18 ) = 1-P (Z <2.18 ) = 0.0193

P-value = 0.0193

= 0.05  

p=0.0193<0.05

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

d) = 0.05

The critical value for a right-tailed test is tc​=1.711.

The rejection region t >1.711

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


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