Independent random samples each containing 70 observations w

Independent random samples, each containing 70 observations, were selected from two populations. The samples from populations 1 and 2 produced 39 and 27 successes, respectively.
Test H 0 :(p 1 ?p 2 )=0 against H a :(p 1 ?p 2 )>0 . Use ?=0.06

(a) The test statistic is ________

(b) The P-value is ___________

Solution

(a) p1=39/70 =0.5571429

p2= 27/70 = 0.3857143

The test statistic is

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.5571429-0.3857143)/sqrt(0.5571429*(1-0.5571429)/70+0.3857143*(1-0.3857143)/70)

=2.06

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(b) It is a right-tailed test.

So the p-value= P(Z>2.06) = 0.0197 (from standard normal table)