a) To determine if there is evidence of a difference in the variability of computer anxiety experienced by males and females, we need to perform an F-test. The F-test compares the variances of two populations. We can calculate the F-statistic by dividing the larger sample variance by the smaller sample variance.
In this case, the sample variances for males and females are given as:
S^2(males) = 13.35
S^2(females) = 9.42
To perform the F-test, we calculate the F-statistic:
F = S^2(males) / S^2(females)
= 13.35 / 9.42
b) To interpret the P-value, we compare it to the significance level (alpha), which is given as 0.05 in this case. If the P-value is less than or equal to the significance level, we reject the null hypothesis. If the P-value is greater than the significance level, we fail to reject the null hypothesis.
c) The assumption we need to make about the two populations in order to justify the use of the F-test is that the populations from which the samples were taken are normally distributed. Additionally, we assume that the populations have equal variances.
d) Based on the results of the F-test, if there is evidence of a difference in the variability of computer anxiety between males and females, we should use an independent samples t-test to test whether there is a significant difference in mean computer anxiety for female and male students.