Question

You wish to test the following claim (Ha) at a significance level of α=0.002. Ho:p1=p2, Ha:p1≠p2 You obtain 344 successes in a sample of size n1=510 from the first population. You obtain 169 successes in a sample of size n2=216from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

a. What is the z-score of the critical value? (Report answer accurate to three decimal places.)

b. Test statistic

Answer 1

Answer:

Given,

It is two tailed test

Ho : p1 = p2,

Ha : p1 ≠ p2

x1 = 344

x2 = 169

n1 = 510

n2 = 216

alpha = 0.002

consider,

p1^ = x1/n1 = 344/510 = 0.6745

p2^ = x2/n2 = 169/216 = 0.7824

p = (x1+x2)/(n1+n2)

= (344+169) / (510+216)

= 0.7066

test statistic = (p1^ - p2^) / sqrt(pq/n1 + pq/2)

= (0.6745 - 0.7824) / sqrt(0.7066*0.2934/510 + 0.7066*0.2934/216)

= -2.92

alpha/2 = 0.002/2 = 0.001

Here the critical value is +/- 3.09

By observing we can say that, test statistic > critical value , so fail to reject the null hypothesis Ho.