Question

P-value is the probability, computed assuming H0 is true, that the test statistic would take a value as extreme or more extreme than that actually observed. Given the sample at hand, it is the smallest level of significance at which H0 would be rejected. It depends on the sample (hypotheses as well) and is hence also a test statistic.

Generate 50 samples of size n=10 from a normal distribution with mean μ=1 and variance σ2=4. For each sample, use the one-sample t test for the hypotheses

H0:μ=1 vs H1:μ≠1

and record the p-value. Please include only a graphical display (stem-and-leaf plot or histogram) of the 50 p-values. Does it convince you that p-value is uniformly distributed on [0,1] if H0 is true?

Answer 1

From the histogram of p value we can say that p value is approximately uniformly distributed.