A manager is interested in which keyboard is the fastest for typing. She randoml

Question

A manager is interested in which keyboard is the fastest for typing. She randomly assigns 36 keyboardists to 4 different groups (all ns = 9). Group 1 types on a Microsoft keyboard, Group 2 types on a Logitech keyboard, Group 3 types on an Apple keyboard, and Group 4 types on an IBM keyboard. The manager records the words per minute typed by each group. The following means and standard deviations were recorded. Test the hypothesis that keyboard affects typing speed. (Hint ANOVA) the alpha is .05

Group

Mean

SD

Group 1 (Microsoft)

91

10

Group 2 (Logitech)

83

2

Group 3 (Apple)

87

6

Group 4 (IBM)

86

6

Group

Mean

SD

Group 1 (Microsoft)

91

10

Group 2 (Logitech)

83

2

Group 3 (Apple)

87

6

Group 4 (IBM)

86

6

Explanation / Answer

here null hypothesis: Ho: keyboard does not affect typing speed(all groups mean typing speed are equal)

alternate hypothesis:Ha:keyboard affects typing speed (Not all groups mean typing speed are equal)

applying one way ANOVA:

here test statistic F=1.99

for 0.05 level and (3,32) df crtiical value of F=2.90

as test statistic is less than critical value we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that   keyboard affects typing speed

c ni x?i S2i ni*(Xi-Xgrand)2 (ni-1)*S2i Group 1 9 91.000 36.000 162.563 288.00 Group 2 9 83.000 16.000 126.563 128.00 Group 3 9 87.000 64.0000 0.563 512.00 Group 4 9 86.000 81.0000 5.063 648.00 grand mean= 86.750 294.750 1576.00 SSTr SSE Source of variation SS df MS F treatment 294.750 3 98.25 1.99 error 1576.000 32 49.25 total 1870.750 35

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