Question

Consider the following hypothesis test.

H₀: p = 0.30

H_a: p ≠ 0.30

A sample of 400 provided a sample proportion p = 0.275.

(a)

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

(b) What is the p-value? (Round your answer to four decimal places.) p-value =_____

(c) At α = 0.05, what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that p ≠ 0.30.

Reject H₀. There is sufficient evidence to conclude that p ≠ 0.30.     

Do not reject H₀. There is sufficient evidence to conclude that p ≠ 0.30.

Do not reject H₀. There is insufficient evidence to conclude that p ≠ 0.30.

(d)

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

test statistic ≤ ______

test statistic ≥ ______

What is your conclusion?

Reject H₀. There is insufficient evidence to conclude that p ≠ 0.30.

Reject H₀. There is sufficient evidence to conclude that p ≠ 0.30.     

Do not reject H₀. There is sufficient evidence to conclude that p ≠ 0.30.

Do not reject H₀. There is insufficient evidence to conclude that p ≠ 0.30.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.30

H_a : p 0.30

n = 400

= 0.275

P₀ = 0.30

1 - P₀ = 1-0.30 = 0.70

a) Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.275 - 0.30 / [0.30*(0.70) /400 ]

= -1.09

b) P(z < -1.091) = 0.2752

P-value = 0.2752

c) = 0.05    

Do not reject Ho.there is insufficient evidence to conclude that p 0.30

d) The critical value for a two-tailed test is z_c​=1.96.

∣z∣ =1.091 ≤ zc​=1.96

Test statistic ≤ 1.091

Do not reject Ho.there is insufficient evidence to conclude that p 0.30