Researchers took random samples of subjects from two populations and applied a two-sample t test to the data using α = 0.10: the P-value for the test, using a nondirectional alternative, was 0.06. For each of the following, say whether the statement is true or false and explain why.
(a) There is a 6% chance that the two population distributions actually are the same.
(b) If the two population distributions actually are the same, then a difference between the two samples as extreme as the difference that these researchers observed would only happen 6% of the time.
(c) If a new study were done that compared the two populations, there is a 6% probability that H0 would be rejected again.
(d) If α = 0.05 and a directional alternative were used, and the data departed from H0 in the direction specified by the alternative hypothesis, then H0 would be rejected.