Question

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

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

Consider the following hypothesis test.

H0: p = 0.20

Ha: 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)

p-value =

(c)

At

α = 0.05,

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

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

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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