Question

Consider the following hypothesis test.

H0: μ ≥ 20

Ha: μ < 20

A sample of 50 provided a sample mean of 19.5. The population standard deviation is 2.

(a) Find the value of the test statistic. (Round your answer to two decimal places.) _______

(b) Find the p-value. (Round your answer to four decimal places.) p-value = _______

(c) Using α = 0.05, state your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ < 20.

Reject H₀. There is insufficient evidence to conclude that μ < 20.      

Do not reject H₀. There is sufficient evidence to conclude that μ < 20.

Do not reject H₀. There is insufficient evidence to conclude that μ < 20.

(d) State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic ≤ ______

test statistic ≥ ______

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ < 20.

Reject H₀. There is insufficient evidence to conclude that μ < 20.      

Do not reject H₀. There is sufficient evidence to conclude that μ < 20.

Do not reject H₀. There is insufficient evidence to conclude that μ < 20.

Answer 1

Solution :

= 20

= 19.5

= 2

n = 50

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    ≥ 20

H_a : < 20

a) Test statistic = z

= ( - ) / / n

= (19.5-20) /3 / 50

= -1.18

b) P(z < -1.179 ) = 0.1193

P-value = 0.1193

c) = 0.05  

Do not reject H_0. There is insufficient evidence to conclude that < 20

d)The critical value for a left-tailed test is z_c​=−1.64.

test statistic ≥ -1.179

Do not reject H_0. There is insufficient evidence to conclude that < 20