Suppose you are analyzing a given data set using a one sample t$-$test at a significance level of $0\mathrm{.}04.$

You decide to do a one$-$tailed test as well as a two$-$tailed test, both at a significance level of $0\mathrm{.}04,$ and

then compare the results. Which of the following statements is CORRECT?

a$)$ The test statistic for the two$-$tailed test will be two times that of the one$-$tailed test.

b$)$ There is a possibility that the two$-$tailed test might reject the null hypothesis while the one$-$tailed

test does not.

c$)$ There is a possibility that the one$-$tailed test might reject the null hypothesis while the two$-$

tailed test does not.

d$)$ The P$-$value for the one$-$tailed test will be two times the P$-$value of the two$-$tailed test.

e$)$ When doing the two$-$tailed test, you must divide the P$-$value of the one$-$tailed test by two to

compare with the alpha $(0\mathrm{.}04).$