Which of the following statements is/are true about the P-value? (True or False)

Question

Which of the following statements is/are true about the P-value?

(True or False) Increasing the distance between the sample mean and the hypothesized mean (the further xbar is from µ0) decreases the P-value because the null is less believable.

(True or False) Decreasing the variance of the population means the xbars should be closer to µ0 and the same distance between the sample mean and the hypothesized mean is less likely so the the P-value decreases and the null is less believable.

(True or False) Increasing the sample size reduces the variance of the xbars so the same distance between the sample mean and the hypothesized mean is less likely and the the P-value decreases and the null is less believable.

Explanation / Answer

It is true, because the distance between the sample mean and the hypothesized mean decreases. It is false, because the p-value increases in this situation. It is false, because the p-value increases too in this situation.

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