Test the hypothesis using a the classical approach and then

Test the hypothesis, using (a) the classical approach and then (b) the P-value approach. Be sure to verify the requirements of the text.

H0: p=0.7 versus H1: p> 0.7

n=250; x=180,?= 0.1

(a) Choose the correct result of the hypothesis test for the classic approach below.

a. Do not reject the null hypothesis, because the test statistic is greater than the critical value

b. Do not reject the null hypothesis, because the test statistic is less than the critical value

c. reject the null hypothesis, because the test statistic is less than the critical value

d. reject the null hypothesis, because the test statistic is greater than the critical value

(b) Choose the correct result of the hypothesis test for the P-value approach below.

a. Do not reject the null hypothesis, because the P-value is less than ?

b. Reject the null hypothesis, because the P-value is less than ?

c.Do not reject the null hypothesis, because the P-value is greater than ?

d. Reject the null hypothesis, because the P-value is greater than ?

Solution

(a) The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(180/250 -0.7)/sqrt(0.7*0.3/250)

=0.69

It is a right-tailed test.

Given a=0.1, the critical value is Z(0.1) =1.28 (from standard normal table)

The rejection region is if Z>1.28, we reject the null hypothesis.

Since Z=0.69 is less than 1.28, we do not reject the null hypothesis.

Answer: b. Do not reject the null hypothesis, because the test statistic is less than the critical value

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(b) The p-value= P(Z>0.69) =0.2451 (from standard normal table)

Answer: c.Do not reject the null hypothesis, because the P-value is greater than ?