A random sample of 10 students contains the following
observations, in hours, for time spent studying in the week before
final exams: 28, 57, 42, 35, 61, 39, 55, 46, 49, 38.
Assume that the population distribution is normal. Test at the
5% significance level the null hypothesis that the population mean
is 40 hours against the alternative that it is higher.
(NOTE: We need to assume that class sizes are normally
distributed in order to use the t distribution because the
sample size n=10 < 25, and the Central Limit Theorem does not
apply.)
A. Since the test statistic equals 1.50, and the critical t
value is 1.833, we fail to reject the null hypothesis and conclude
that there is not enough evidence to determine that hours of work
is truly higher than 40 hours/week.
B. Since the test statistic equals 1.83, and the critical t
value is 1.50, we reject the null hypothesis and conclude that
there is enough evidence to determine that hours of work is higher
than 40 hours/week.
C. Since the test statistic equals 1.50, and the critical t
value is 2.262, we fail to reject the null hypothesis and conclude
that there is not enough evidence to determine that hours of work
is truly higher than 40 hours/week.
D. Since the test statistic equals 1.50, and the critical t
value is 1.812, we fail to reject the null hypothesis and conclude
that there is not enough evidence to determine that hours of work
is truly higher than 40 hours/week.