Conduct the hypothesis test and provide the test statistic, critical value, and/

Question

Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion.

American Idol: The contestants on the TV show American Idol try to win a singing contest. At one point, the web site WhatNotToSing.com listed the actual numbers of eliminations for different orders of singing, and the expected number of eliminations was also listed. The results are in the table below. Use a 0.05 significance level to test the claim that the actual eliminations agree with the expected numbers. Does there appear to be support for the claim that the leadoff singers appear to be at a advantage?

SInging Order 1 2 3 4 5 6 7through12

Eliminations 20 12 9 8 6 5 9

Expected Eliminations 12.9 12.9 9.9 7.9 6.4 5.5 13.5

Explanation / Answer

The test statistic chi square is:

Sum over(Oi-Ei)^2/Ei

=(20-12.9)^2/20+…+(5-5.5)^2/5.5

=5.62

The P-Value is 0.467073. The result is not significant at p < 0.05.

The P value is greater than 0.05. Thus fail to reject the null hypothesis. Thus there is not sufficient evidence to support the claim that the leadoff singers appear to be at a advantage.

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