Question

You may need to use the appropriate appendix table or technology to answer this question.

Consider the following hypothesis test.

*H*_{0}: * p* = 0.20

*H*_{a}: * p* ≠ 0.20

A sample of 500 provided a sample proportion

*p* = 0.175.

(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* ≠ 0.20.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.20. Reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.20.Reject *H*_{0}. There is
sufficient evidence to conclude that *p* ≠ 0.20.

(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* ≠ 0.20.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.20. Reject
*H*_{0}. There is insufficient evidence to conclude
that *p* ≠ 0.20.Reject *H*_{0}. There is
sufficient evidence to conclude that *p* ≠ 0.20.

Answer #1

a)

Test statistic,

z = (pcap - p)/sqrt(p*(1-p)/n)

z = (0.175 - 0.2)/sqrt(0.2*(1-0.2)/500)

z = -1.40

b)

P-value Approach

P-value = 0.1615

c)

As P-value >= 0.05, fail to reject null hypothesis.

.Do not reject H0. There is insufficient evidence to conclude that
p ≠ 0.20.

d)

This is two tailed test, for α = 0.05

Critical value of z are -1.96 and 1.96.

Hence reject H0 if test statistic < -1.96 or test statistic > 1.96

.Do not reject H0. There is insufficient evidence to conclude that p ≠ 0.20.

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