Answer:
iii. The data do not provide sufficient evidence to conclude that the mean number of minutes exercised per week is larger for men than for women at this gym
Step-by-step explanation:
1) The hypotheses are
H0: u1 ≤ u2 against the claim Ha: u1 > u2
The men spend less or equal time than the women at the gym each week
vs
the men spend greater time than the women at the gym each week
2) The test statistic is
t= (x1`- x2`) / √ s1²/n1+ s2²/n2
t= 65.7- 64.8/√(13.9)²/75 + (9.6)²/68
t= 0.9/√2.57613 +1.35529
t=0.4539
and the degrees of freedom is
3) υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
=[(13.9)²/75 + (9.6)²/68]²/ [(13.9)²/75 ]² /74 + [ (9.6)²/68]²/67
= 139
The degrees of freedom is always rounded in this calculation
4) The Critical region is [1.656, ∞]
5) t-score is outside of the critical region, so there is not enough evidence to reject H₀.
iii. The data do not provide sufficient evidence to conclude that the mean number of minutes exercised per week is larger for men than for women at this gym
