The Computer Anxiety Rating Scale (CARS) measures an individuals 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 are differences in the amount of computer
anxiety experienced by students with different majors. They found the following.

Source Degree of freedom Sum of Square Mean Square(Variance) F
_____________________________________________________________________________
Among majors 5 3,172
Within majors 166 21,246
________ _________
Total 171 24,418

Major n Mean
_______________________________________________________________________________
Marketing 19 44.37
Management 11 43.18
Other 14 42.21
Finance 45 41.80
Accountancy 36 37.56
MIS 47 32.21



(a). Complete the ANOVA summary table
(b). At 0.05 level of significance, is there evidence of difference in the
mean computer anxiety experienced by different majors?
(c). If the results in (b) indicate that it is appropriate, use the Tukey-Kramer
procedure to determine which majors differ in mean computer anxiety. Discuss your
findings.

Your ANOVA summary table should have the following setup:

Source.....SS.....df.....MS.....F
Between
Within
Totals

Fill in the data with what you know, then find what you don't know.

Here are a few hints:
SS total = SS between + SS within

To calculate df between:
k - 1
Note: k = number of levels or groups.

To calculate df within:
N - k
Note: N = total number of values in all levels or groups.

df total = df between + df within

To calculate MS between:
SS between/df between

To calculate MS within:
SS within/df within

To calculate F-ratio:
MS between/MS within

After filling in the table and finding the F-ratio, find the critical or cutoff value to reject the null using an F-table. Compare to the F-ratio to determine whether or not to reject the null. If the null is rejected, there is a difference. If the null is not rejected, there is no difference.

If you need to use the Tukey procedure, compare all possible pairs of means to determine which majors differ.

I hope this brief summary will get you started.

(a) The ANOVA summary table can be completed using the given information:

Source Degree of freedom Sum of Square Mean Square(Variance) F
_____________________________________________________________________________
Between groups 5 3,172 634.4 ?
Within groups 166 21,246 128.1
________ _________
Total 171 24,418

To calculate the value of F, we need the mean square for "Between groups" and "Within groups".

Mean Square (Between groups) = Sum of Square (Between groups) / Degree of freedom (Between groups)
= 3,172 / 5
= 634.4

Mean Square (Within groups) = Sum of Square (Within groups) / Degree of freedom (Within groups)
= 21,246 / 166
= 128.1

Since we don't have the value of F, we cannot determine its significance yet.

(b) To determine if there is evidence of a difference in the mean computer anxiety experienced by different majors, we need to perform a hypothesis test. At the 0.05 level of significance, we compare the calculated F value to the critical F value.

The null hypothesis (H0) is that there is no difference in the mean computer anxiety experienced by different majors.
The alternative hypothesis (Ha) is that there is a difference in the mean computer anxiety experienced by different majors.

If the calculated F value is greater than the critical F value, we reject the null hypothesis and conclude that there is evidence of a difference in means. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a difference in means.

(c) We cannot proceed with the Tukey-Kramer procedure without knowing the significance of the F statistic. Therefore, we cannot determine which majors differ in mean computer anxiety at this time.

(a) To complete the ANOVA summary table, we need to fill in the missing values for the Sum of Squares and Mean Square columns.

Source Degree of freedom Sum of Square Mean Square(Variance) F
_____________________________________________________________________________
Among majors 5 3,172 3,172/5 = 634.4
Within majors 166 21,246 21,246/166 = 127.9
________ _________
Total 171 24,418

(b) To test if there is evidence of a difference in the mean computer anxiety experienced by different majors, we need to perform an F-test.

The null hypothesis (H0) is that there is no difference in the mean computer anxiety experienced by different majors. The alternative hypothesis (Ha) is that there is a difference.

Using the F-test, we compare the computed F value with the critical F value from the F-distribution table. If the computed F value is greater than the critical F value, we reject the null hypothesis.

In this case, the computed F value is 634.4 (from the ANOVA summary table) and the critical F value can be found from the F-distribution table with degrees of freedom (df1 = 5 and df2 = 166) at the 0.05 level of significance.

If the computed F value is greater than the critical F value, we reject the null hypothesis and conclude that there is evidence of a difference in the mean computer anxiety experienced by different majors.

(c) If there is evidence of a difference in mean computer anxiety, we can use the Tukey-Kramer procedure to determine which majors differ from each other.

The Tukey-Kramer procedure is a post hoc test that allows us to compare all possible pairs of means and determine if they are significantly different.

To use the Tukey-Kramer procedure, we calculate the Tukey-Kramer critical value based on the total number of comparisons (k) and the degrees of freedom within majors (dfw).

In this case, k = 6 (number of majors) and dfw = 166 (degrees of freedom within majors).

Once we have the Tukey-Kramer critical value, we compare the difference between means for each pair of majors with the critical value. If the absolute difference between means is greater than the critical value, we conclude that there is a significant difference between the means.

By comparing the mean computer anxiety for each pair of majors, we can determine which majors differ in mean computer anxiety.

Please note that in order to perform the calculations required in steps (b) and (c), you'll need to use a statistical software or a calculator with the capability to perform ANOVA and Tukey-Kramer tests.