Anova Problems

1. The science of ergonomics studies the influence of human factors in technology. With the widespread use of computers for dat 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 identitical 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. The secretaries all had about the same level of experience, typing speed, and computer skills. The time (in minutes) taken to complete the task was observed.

   Group 1 Menu-Driven	Group 2 Command-Driven	Group 3 Mixed
   12	14	10
   15	11	8
   12	12	10
   10	11	7
   11	13	9
   13	14	8

   1. Does the type of wordprocessing program used affect performance? The null hypothesis is there is no difference between the three types of programs, stated as the average time to complete the task is the same in all cases.

   2. If the secretaries had different levels of experience, typing speed, and computer skills, how would it affect the data? Would it be an extraneous source of variation or noise? Would this increase the within-sample variation or between-sample variation?

2. The table below contain the results of an experiment involving fifteen programmers randomly assigned to implement an algorithm in a specified programming language. The outcome variable is the number of lines of code.

   Group 1 Language X	Group 2 Language Y	Group 3 Language Z
   144	101	130
   120	144	180
   176	211	141
   288	288	374
   144	72	302

   1. The null hypothesis is ?

   2. Does the data support or reject the null hypothesis at the .01 level?

   3. If the programmers had different levels of experience with the language, how would it affect the data? Would it be an extraneous source of variation or noise? Would this increase the within-sample variation or between-sample variation?

3. Engineering has completed the design of a handheld security device that will be sold to DoD contractors. The unit contains a battery to sustain volatile memory over time. There are four battery supplies whose products you are considering. Past experience indictes that battery lifetimes are normally distributed. You conduct an experiment using six batteries of each brand. Each of the batteries are placed in a test device that slowly drains the battery power and records the number of hours the unit provide power.

   Brand 1	Brand 2	Brand 3	Brand 4
   41	32	35	33
   35	37	30	27
   48	46	24	36
   40	53	26	35
   45	41	28	27
   52	43	31	25

   1. Does the data support or reject the null hypothesis, at the .01 level, that average battery lifetimes are the same?

   2. What issues would you raise regarding the conduct of this experiment?

4. An information systems researcher wishes to determine whether the type of help system available to programmers has an effect on the time required to write a program. The research knows that programmer experience can influence the time (in minutes) require to write a program. An experiment is set up with three different help systems and four levels of programming experience. (1-low experience, practically no experience, 2-no more than two years, 3-less than five years but more than two years, and 4-more than five years). The mean times for each help system and experience level is provided.

   Experience	HelpA	HelpB	HelpC
   1	32 34.5 29 28.5	42 31.5 33 33.5	42 29 44.5 42.5
   2	27.5 43.5 29.5 31.5	31 30 29.5 31.5	32 29 28.5 32.5
   3	24.5 25.5 24 30	22.5 25.5 22.5 31.5	21 23 20 30
   4	22 23.5 21 31.5	24.5 22 25 22.5	15 25 16.5 15.5

   1. Is there an interaction effect?

   2. What factors are significant? Can you trace the items that may be causing significance? Is it significant at the .05 or .01 level?