a)
The null and alternative hypotheses are
H0:μ1=μ2
Ha:μ1>μ2
The degrees of freedom df=n1+n1-2=30+30-2=58 and alpha=0.01
The critical value tc=2.392.
The rejection region R={t:t>2.392}
The t-statistic is
t
X1  X 2
(n1  1) s12  (n2  1) s22 1 1
(  )
n1  n2  2
n1 n2

37.6  55.8
(30  1)38.492  (30  1)48.262 1
1
(  )
30  30  2
30 30
 1.615
Since t=−1.615≤tc=2.392, it is then concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the males on average have a better sense of
direction than females.
b) df=58
p value=0.9941
c) Difference between means=37.6-55.8= -18.2
Margin of error E is given by
E  tc
(n1  1) s12  (n2  1) s22 1 1
(30  1)38.492  (30  1)48.262 1
1
(  )  2.392 *
(  )  26.96
n1  n2  2
n1 n2
30  30  2
30 30
Confidence interval is (-18.2-26.96, -18.2+26.96)=(-45.16, 8.76)
d) We are 95% confident the difference between the population mean absolute painting errors for
male and females lies between -45.16 and 8.76.
Yes. It support the conclusion of a) because the confidence interval contain 0. That means null
hypothesis is not rejected.