The Computer Anxiety Rating Scale (CARS) measures an individual's level of computer anxiety, on a scale from 20 ( no anxiety) to 100 (highest level of anxiety). Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine whether there is a difference between the level of computer anxiety experienced by female students and male students. They found the following:

Question

The Computer Anxiety Rating Scale (CARS) measures an individual's level of computer anxiety, on a scale from 20 ( no anxiety) to 100 (highest level of anxiety). Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine whether there is a difference between the level of computer anxiety experienced by female students and male students. They found the following:

Males Females (sample mean)X: 40.26 36.85
S 13.35 9.42
N 100 72

a) at the 0.05 level of significance, is there evidence of a difference in the variability of the computer anxiety experienced by males and females?
b) Interpret the P-Value
c) What assumption do you need to make about the two populations in order to justify the use of the F test?
d) Based on (a) and (b) which t test defined in section 10.1 should you use to test whether there is a significant difference in mean computer anxiety for female and male students?

Answer 1

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.