Question

A poll suggests that the Democrat candidate for one of the congressional seats in the state won 450 of the 1,000 respondents whereas the Republican candidate won 459 of the 1,000 respondents. Test the (null) hypothesis that the winning percentage (proportion) for these two candidates are the same at 1% of significance level.

Answer #1

Given that,

For Democrat candidate : n1 = 1000, x1 = 450 and

For Republican candidate : n2 = 1000, x2 = 459 and

The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

Pooled proportion is,

Test statistic is,

=> Test statistic = Z = **-0.40**

p-value = 2 * P(Z < -0.40) = 2 * 0.3446 = 0.6892

=> p-value = **0.6892**

Since, p-value is greater than level of significance of 0.01, we fail to reject the null hypothesis.

Therefore, there is **not** sufficient evidence to
warrant rejection of the claim that the winning percentage
(proportion) for these two candidates are the same at 1% of
significance level.

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