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Truth p~ Two samples are drawn to test the hypothesis,Ho: p= 0.5us H4: p0.5. One sample...

Truth p~ Two samples are drawn to test the hypothesis,Ho: p= 0.5us H4: p0.5. One sample has size n 250 and the other has size n=125. Both samples yield the same sample proportion of 0.4.Consider the statement:The samples will produce the different p-values for the hypothesis test above.. Is this statement always true, sometimes true or never true?

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Answer #1

The sample size impacts the standard error.

SE = sqrt(p*(1-p)/n)

Hence higher the value of n, less will be the value of SE. This will increase the value of z.

Higher z-values will results into lower p-value.

Hence the above statement is always true.

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