Question

The Computer Anxiety Rating Scale (CARS) measures a person's computer anxiety, on a scale from 20 (none) to 100 (highest). Researchers administered CARS to 124 students in order to determine whether there are differences in the amount of computer anxiety for students with diferent majors. They found the results below. Complete parts (a) through (c). Click the icon to view the results. Click on the icon to view a partial table of critical values associated with a 0.05 of the Studentized Range, Q. a. Complete the ANOVA summary table. Mean Source Among majors3 Within majors Degrees of Sum of 1,950 1205,600 FreedomSquaresSquares Total 123 17,550

Answer 1

Solution:

We are given following incomplete ANOVA table:

Sum of Squares 1,950 15,600 17,550 Degrees of Freedom Mean Squares Source Among majors Within majors Total 120 123 Major Marketing Management Finance 23 23 23 Mean 47.44 40.06 39.15 31.96

We have to complete above ANOVA table.

Mean Squares:

MSB = Mean Square Between ( Among ) Majors

Sum of Squares between Majors = SSB = 1950

df_between = 3

Thus

MSB = SSB / df_between

MSB = 1950 / 3

MSB = 650

MSW = Mean squares within majors

SSW = Sum of squares within majors = 15600

df_within = 120

Thus

MSW = SSW / df_within

MSW = 15600 / 120

MSW = 130

F test statistic( F ratio) is given by formula:

F = MSB / MSW

F = 650 / 130

F = 5

Thus we get:

Source	Degrees of freedom	Sum of Squares	Means Squares	F
Among Majors	3	1950	650	5
Within Majors	120	15600	130
Total	123	17550

To find F critical value, we use given table.

Look in the table for df Numerator = 3 and df denominator = 120 and find F critical value.

var3 vard Critical Values of the Studentized Rang var2 Upper 5% Points (alpha-0.05) Degrees of Freedom in the Numerator Degrees of Freedom in the Denominato 17.9726.9832.82 6.09 4.5 3.93 3.64 3.46 3.34 3.26 3.2 3.15 3.11 3.08 3.06 3.03 3.01 9.8 6.83 5.76 5.22 4.9 4.68 4.53 4.42 4.33 4.26 4.2 4.15 4.11 4.08 4.05 4.02 5.9 5.0 13 15 16 17 2.98 2.97 2.96 2.95 2.92 2.89 2.86 3.98 3.96 24 3.49 3.44 3.4 3.36 3.31 3.85 3.79 3.74 3.69 3.63 40 infinite 2.77

F critical value = 3.36

Decision criteria:

Reject null hypothesis H0, if F test statistic > F critical value, otherwise we fail to reject H0.

Since F test statistic value = 5 > F critical value = 3.36, we reject H0.

Thus we conclude that: at least one of majors has different mean.