Question

Consider the following hypothesis test.

H₀: p = 0.30

H_a: p ≠ 0.30

A sample of 500 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?

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

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

Answer 1

The statistical software output for this problem is :

Test statistics = -1.22

P-value = 0.2225

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

test statistic ≤ -1.96 test statistic ≥ 1.96

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