Question

5.66 Exercise and Gender The dataset Exercise- Hours contains information on the amount of exercise (hours per week) for a sample of statis- tics students. The mean amount of exercise was 9.4 hours for the 30 female students in the sample and 12.4 hours for the 20 male students. A randomiza- tion distribution of differences in means based on these data, under a null hypothesis of no difference in mean exercise time between females and males, is centered near zero and reasonably normally

Answer 1

Ho: there is no difference in the mean exercise time for females and males.
H1: the mean exercise time for females is less than males.

Test statistic, t = (Xbar1 - Xbar2)/SE
t = (9.4-12.4)/2.38
t = -1.2605

df = (s1^2/n1 + s2^2/n2)^2 / ((s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1))
df = (0.2439+0.3408)^2 / ( 0.2439^2/(30-1) + 0.3408^2/(20-1) )
df = 42

p-value = P(T<t)
p-value = (1-P(T<-1.2605)
p-value = T.DIST(-1.2605,42,TRUE)
p-value = 0.107223559

With t(42) = -1.2605, p>5%, i fail to reject Ho and conclude that there is no difference in the mean exercise time for females and males.