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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 <0.5H0: p = 0.5 vs HA: p <0.5 n1=n2=123n1=n2=123

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?

math   Statistics-And-Probability   
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Answer #1

If no. of successes i.e. x is same for two samples then the sample proportions are same and hence the samples will produce same p-values otherwise the samples will produce different p-values. Since no. of successes may not be same always so this statement is sometimes true.

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