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

Question #120483
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
1
Expert's answer
2020-06-10T19:56:02-0400

Use a t-statistic, with degrees of freedom df=n1df=n−1


 for inference for a population mean:


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


whereSE=s/nwhere SE=s/\sqrt n


Use a t-statistic, with degrees of freedom df=ndiff1df=n_{diff}−1  for inference for the difference in two paired (dependent) means:

CI:xdiff±tdf/SECI: x_{diff}±t^∗_{df}/SE


SE=s/nSE=s/\sqrt n Note that μdiffμ_{diff} is often 0, since often H0:μdiff=0.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



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