Answer to Question #120483 in Statistics and Probability for Joseph Se

Question

For given values of the sample mean and the sample standard deviation when n = 25, you conduct a hypothesis test and obtain a p-value of 0.0667, which leads to non-rejection of the null hypothesis. What will happen to the p-value if the sample size increases (and all else stays the same)?

A. Increase
B. Stay the same
C. Decrease
E. May either increase or decrease

Answer 1

Use a t-statistic, with degrees of freedom $df=n−1$

 for inference for a population mean:

$CI: x¯±t^{∗}_{df}SE$ $HT: Tdf\frac{x¯−μ}{SE}$

$where SE=s/\sqrt n$

Use a t-statistic, with degrees of freedom $df=n_{diff}−1$  for inference for the difference in two paired (dependent) means:

$CI: x_{diff}±t^∗_{df}/SE$

$SE=s/\sqrt n$ Note that $μ_{diff}$ is often 0, since often $H_{0}:μ_{diff}=0 .$

As the sample size increases the standard error will decrease, which increases the test statistic, and hence decreases the p-value