You hear on the local news that for the city of Kalamazoo, the proportion of peo

Question

You hear on the local news that for the city of Kalamazoo, the proportion of people who support President Obama is 0.55. However, you think it is greater than 0.55. The hypotheses for this test are Null Hypothesis: p 0.55, Alternative Hypothesis: p > 0.55. If you randomly sample 24 people and 14 of them support President Obama, what is your test statistic and p-value?

1) Test Statistic: 0.328, P-Value: 0.371

2) Test Statistic: -0.328, P-Value: 0.629

3) Test Statistic: -0.328, P-Value: 0.371

4) Test Statistic: 0.328, P-Value: 0.629

5) Test Statistic: 0.328, P-Value: 0.742

Explanation / Answer

P = 0.55

p = 14/24 = 0.5833

n = 24

= sqrt[ P * ( 1 - P ) / n ] = sqrt(0.55 * 0.45 / 24) = 0.1016

z = (p - P) / = (0.5833 - 0.55) / 0.1016 = 0.328

P-value = P(Z > 0.33) = 1 - P(Z < 0.33) = 1 - 0.6293 = 0.3707

Option-1) Test Statistic: 0.328, P-Value: 0.371

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