10 Test the hypothesis using the Pvalue approach Be sure to

10) Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.

H0: p = 0.53 versus H1: p < 0.53

n = 150, x = 72, a = 0.01

A) Is np0 (1-p0) greater than or equal to 10? Yes or No?

B) P-Value = _ (Round to three decimal places as needed.)

C) Should the hypothesis be rejected or no? Is the reasoning because the P-value is greater than or less than a?

Solution

A)

n*p*(1-p) = 150*0.53*(1-0.53) = 37.365

Yes, this is greater than 10.

B)

P_bar= 72/150 = 0.48

standard deviation of sampling distribution, sigma= sqrt(p*(1-p)/n)) = sqrt(0.53*(1-0.53)/150) =0.04075

z-score = (p_bar -p)/sigma =(0.48-0.53)/0.04075 = -1.2269

p-value = Cumulative probability: P(Z < -1.2269) = 0.110

C)

since p-value is greater than a= 0.01,

we should not reject the null hypothesis.