Question

The science of ergonomics studies the influence of "human factors” in technology, i.e., how human beings relate to and work with machines. With the widespread use of computers for data processing, computer scientists and psychologists are getting together to study human factors. One typical study investigated the productivity of secretaries with different word processing programs. An identical task was given to 18 secretaries, randomly allocated to three groups. Group 1 used a primarily menu-driven program. Group 2 used a command-driven program, and Group 3 used a mixture of both approaches. MINITAB produced the following ANOVA. Use it to answer the questions below. One-way ANOVA: Group1, Group2, Group3

Source	DF	SS	MS	F
Factor	1	0.97336	0.97336	2026.95
Error	18	0.00864	0.00048
Total	19	0.98200

S = 0.02191 R-Sq = 99.1% R-Sq(adj) = 99.1% ?0.01 /(1,18) = 8.2854

A. Test the Null Hypothesis that the true mean time is the same for all three groups. As always, clearly state the null and alternative hypotheses. Use a 0.01 level of significance. Show clearly how you make your decision. What conclusion would you arrive at? Make sure you use wording that would make your Statistic teacher happy and then phrase your answer so that a “friend” would understand what your conclusions are.

Answer 1

Ans:

Group 1 used a primarily menu-driven program.

Group 2 used a command-driven program, and

Group 3 used a mixture of both approaches.

Null Hypothesis : There is no significant difference in the true mean time of all the three groups.

Alternative Hypothesis : Atleast one group is significant differe in the true mean time of the two groups or All groups are siginificant differe.

Output Given

Source	DF	SS	MS	F
Factor	1	0.97336	0.97336	2026.95
Error	18	0.00864	0.00048
Total	19	0.98200

In this table the calculated value of F = 2026.95

and  S = 0.02191 R-Sq = 99.1% R-Sq(adj) = 99.1% ?0.01 /(1,18) = 8.2854

The tabulated value of F = 8.2854 at 1% level of significance and 1 and 18 df.

Since for the testing of hypotheis we see that the calculated value of F is greater than the tabulated value of F i.e (2026.95 > 8.2854) since we can reject the null hypothesis and conclude that Atleast one group is significantly differe in the true mean time from the other groups or All groups are siginificant differe. Further which groups are significantly differ can be find using post hoc analysis as per available data set. On the basis of the output the only conclusion will be drawn that null hypotheis would we rejected .