Decide whether the normal sampling distribution can be used. If it can be used l

Question

Decide whether the normal sampling distribution can be used. If it can be used lest, the claim about the population proportion p at the given level of significance alpha using the given sample statistics. Claim p notequalto 0.28 alpha = 0.05, Sample statistics p = 0.25, n = 160 Can the normal sampling distribution be used? A. No, because np is less than 5. B. Yes, because pq is greater than alpha = 0.05. C. No, because nq is less than 5. D. Yes, because both np and nq are greater than or equal to 5.

Explanation / Answer

(a) Option D

(b)

Data:    

n = 160   

p = 0.28   

p' = 0.25   

Hypotheses:    

Ho: p = 0.28   

Ha: p 0.28   

Decision Rule:    

= 0.05   

Lower Critical z- score = -1.9600   

Upper Critical z- score = 1.9600   

Reject Ho if |z| > 1.9600   

Test Statistic:    

SE = {p (1 - p)/n} = (0.28 * (1 - 0.28)/160) = 0.0355

z = (p'- p)/SE = (0.25 - 0.28)/0.0354964786985977 = -0.8452

p- value = 0.3980   

Decision (in terms of the hypotheses):    

Since 0.8452 < 1.9600 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that p 0.28.   

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