Sample Hypothesis Test - Proportion

Question

You wish to test the following claim () at a significance level of .      

      

You obtain 339 successes in a sample of size  from the first population. You obtain 173 successes in a sample of size  from 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.

What is the critical value for this test? (Report answer accurate to three decimal places.)critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

test statistic = 

Answer 1

Since this is a right-tail test, the critical value is z such that:

P(Z > z) = 0.99. That z is 2.33.

Need to compute z-statistic.

x1 = 339 and x2 = 173 (number of successes)

Individual sample proportions: p1 = x1/n1; p2 = x2/n2

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

Test statistic is z = (p1-p2) - 0

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sqrt(p*(1-p)*(1/n1)+(1/n2))