17 In a recent poll 807 adults were asked to identify their

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In a recent poll, 807 adults were asked to identify their favorite seat when they fly, and 519 of them chose a window seat. Use a 0.05?significance level to test the claim that the majority of adults prefer window seats when they fly. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

HO: P is < or, < or, = or, not = to 0.5 ?____

H1: P is < or, < or, = or, not = to 0.5?_____

The P value is_____

(round to 4 deimal places)

The critical z value is______

(round to 4 deimal places)

Solution

HO: P is = 0.5

H1: P > to 0.5

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The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(519/807-0.5)/sqrt(0.5*0.5/807)

=8.13

It is a right-tailed test.

So the p-value = P(Z>8.13) =0 (from standard normal table)

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Given a=0.05, the critical value is Z(0.05)=1.6449 (from standard normal table)