Question

Test the hypothesis, using (a) the classical approach and then (b) the P-value approach. Be sure to verify the requirements of he test. Ho p 0.6 vsus H p>0.6 n 100; x- 75, a-0.05 a) Choose the correct result of the hypothesis test for the classic approach below. OA. Do not reject the null hypothesis, because the test statistic is greater than the critical value B. O C. Reject the null hypothesis, because the test statistic is greater than the critical value O D. Reject the null hypothesis, because the test statistic is less than the critical value b) Choose the correct result of the hypothesis test for the P-value approach below. Do not reject the null hypothesis, because the test statistic is less than the critical value. A. Do not reject the null hypothesis, because the P-value is greater than α. OB. Reject the null hypothesis, because the P-value is greater than a C. Reject the null hypothesis, because the P-value is less than α Do not reject the null hypothesis, because the P-value is less than α. D.

Answer 1

Sample proportion $\hat{p}$ = 75/100 = 0.75

Test statistics

z = $\hat{p}$ - p / sqrt(p(1-p) / n)

= 0.75 - 0.6 / sqrt( 0.6 * 0.4 / 100)

= 3.06

a)

Critical value at 0.05 level is 1.645

Reject the null hypothesis.because test statistics is greater than critical value.

b)

p-value = P(Z > z)

= P( Z > 3.06)

= 0.0011

Reject the null hypothesis because p-value is less than $\alpha$