Question

# You wish to test the following claim (H a) at a significance level of α = 0.02.

You wish to test the following claim (${H}_{a}$) at a significance level of $\alpha =0.02$.

${H}_{o}:{p}_{1}={p}_{2}$
${H}_{a}:{p}_{1}<{p}_{2}$

You obtain 380 successes in a sample of size ${n}_{1}=641$ from the first population. You obtain 179 successes in a sample of size ${n}_{2}=259$ 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 test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

This test statistic leads to a decision to...

As such, the final conclusion is that...

Solution :

Given that,

This a left (One) tailed test.

Critical value of  the significance level is α = 0.02, and the critical value for a two-tailed test is = -2.054 = x / n = 423 / 558 = 0.76

Test statistics

z = ( - ) /  *(1- ) / n

= ( 0.76 - 0.77) / (0.77*0.23) / 558

-0.561

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