Answer
a)$s_1^2=43.56cm^2$
$s_2^2=36.2404cm^2$
b)$H_0=\sigma_1=\sigma_2$
c)$1.202.$
d) There is not sufficient evidence to support the claim that heights of men and heights of women have different variances.
Work Step by Step
a) We know that the sample variance is equal to the sample standard deviation squared. Hence:
$s_1^2=(6.6cm)^2=43.56cm^2$
$s_2^2=(6.02cm)^2=36.2404cm^2$
b) The null hypothesis says that the population variances are equal: $H_0=\sigma_1=\sigma_2$
c) The value of the F, the test statistic is the ratio of the sample variances:
$F=\frac{s_1^2}{s_2^2}=\frac{43.56}{26.2404}=1.202.$
d) If $P$ is less than the significance level, we reject the null hypothesis. $P=0.2550\gt0.10$, hence we fail to reject the null hypothesis. Hence there is not sufficient evidence to support the claim that heights of men and heights of women have different variances.
