Question

A publisher reports that 67%67% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 380380 found that 63%63% of the readers owned a personal computer. Make the decision to reject or fail to reject the null hypothesis at the 0.010.01 level.

a) reject null hypothesis

b) fail to reject null hypothesis

Answer 1

Data:    

n = 380   

p = 0.67   

p' = 0.63   

Hypotheses:    

Ho: p = 0.67   

Ha: p ≠ 0.67   

Decision Rule:    

α = 0.01   

Lower Critical z- score = -2.5758   

Upper Critical z- score = 2.5758   

Reject Ho if |z| > 2.5758   

Test Statistic:    

SE = √{p (1 - p)/n} = √(0.67 * (1 - 0.67)/380) = 0.0241

z = (p'- p)/SE = (0.63 - 0.67)/0.0241214034679402 = -1.6583

p- value = 0.0973   

Decision (in terms of the hypotheses):    

Since 1.6583 < 2.5758 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that the percentage is different from 67%   

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