c. P-value = 0.495
d. The relationship is not statistically significant
20. The test here is the independent samples t-test. Hence, the null hypothesis and alternative
Null hypothesis: There is no significant di
erence between the two means from the two populations.
Alternative hypothesis: There is a significant di
erence between the two means from the two
From the critical values of the t table, we get 40 degrees of freedom and a 0.05 level of significance;
the critical value of t is 2.0211.
Since the obtained value of t is +4.55, which is greater than the critical value of t, which is 2.0211, the
null hypothesis is rejected. Hence, the alternative hypothesis may be accepted.
Thus, we may conclude that the di
erence between the two populations is significant.
a. Increasing the sample size, increasing the significance level, reducing the measurement error
b. Maximizing the power minimizes the type II error of the procedure. This means that the
probability of accepting the null hypothesis when the alternative hypothesis is true is reduced to the
minimum. This would mean an increase in the type II error. So, the power is generally maximized by
keeping the type I error at a fixed level.