Osei, at the age of eleven, established a mean time of 15.43 seconds for swimming the 30-yard
freestyle, with a standard deviation of 0.90 seconds. His father, Attakora, speculated that Osei could
improve his time with the aid of goggles. Consequently, Attakora procured a new pair of goggles for
Osei and proceeded to time Osei for 20 separate 30-yard freestyle swims. Across these 20 swims, Osei
attained a mean time of 14.80 seconds. Attakora interpreted this improvement as evidence that the
goggles facilitated Osei in swimming faster than his previous mean time of 15.43 seconds. To ascertain
the significance of this improvement, a hypothesis test is conducted with a predetermined \alpha level of
0.05. It is assumed that the swim times for the 30-yard freestyle follow a normal distribution.
a. Would you describe the above hypothesis test as a one-tail test or two-tail test? Justify your
answer.
b. State the null hypothesis and the alternate hypothesis.
c. Select the level of significance.
d. Select the test statistic.
e. Formulate the decision rule.
f. Make a decision and interpret the result.