Researchers used a random sample of size 100 to test the null hypothesis that the average difference between the household income of immigrant women and their adult daughters is equal to 0. Their decision rule was to reject the null hypothesis if the two sided P value is less than α. Suppose that the population mean is, in fact, $500 and the standard deviation is known to be $5,000. Calculate the probability that they will

a. reject the null hypothesis if α = 0.05. If α = 0.01.

b. not reject the null hypothesis if α = 0.05. If α = 0.01.