Question

Consider the following hypothesis test.

*H*_{0}: * 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 *H*_{0}. There is sufficient
evidence to conclude that *p* ≠ 0.30.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.30. Reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.30.Reject *H*_{0}. 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 *H*_{0}. There is sufficient
evidence to conclude that *p* ≠ 0.30.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.30. Reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.30.Reject *H*_{0}. 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 *H*_{0}. There is insufficient
evidence to conclude that *p* ≠ 0.30.

test statistic ≤ -1.96 test statistic ≥ 1.96

Do not reject *H*_{0}. There is insufficient
evidence to conclude that *p* ≠ 0.30.

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