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Truth p ~ Two samples are drawn to test the hypothesis, H0: p = 0.5 vs...

Truth p ~ Two samples are drawn to test the hypothesis, H0: p = 0.5 vs HA: p <0.5 n1=n2=123 However, the samples yield different sample proportions.

Consider the statement:

The samples will produce different p-values for the hypothesis test above.

Is this statement always true, sometimes true or never true?

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Answer #1

For testing the hypothesis

Ho : p = 0.5

Ha : p < 0.5

we calculate the test statistic as given below

where p = 0.5          ,,, population proportion

p̂ is the sample proportion

and n is the sample size

For the 2 samples under consideration

n is same which is equal to 123

p is same which is equal to 0.5

but

p̂ which is the sample proportion is different

Hence, the value of test statistic z would be different

Since the z score is different, the p-value has to be different

Hence, the samples will produce different p-values for the hypothesis test above.

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