Is this a paired design or a two independent samples design?

Questions 36 through 42 are based on the following scenario.

A human factors engineer wanted to compare two different stove designs with respect to how many errors are made by consumers when using the stove. The 20 women subjects available for her experiment were first matched on a series of extraneous variables which the engineer felt were important. One member of each pair was randomly selected and assigned to use stove design 1, and the remaining member of each pair was assigned to use stove design 2. Stove design 1 had the burners placed in a pattern such that the control knobs were directly below each burner. Stove design 2 had the burners in two rows and the knobs were below the burners but not spatially aligned. (See diagram below.) The engineer felt that design 2 would lead to more errors. During the experiment the subjects were asked to do a series of cooking tasks while simulating a home environment with three hungry children under the age of six. The subjects had to perform other tasks while cooking, such as, getting out juice, crackers, answering the phone, etc. The data are presented below.

Pair

1

2

3

4

5

6

7

8

9

10

Errors with Design 1

2

1

3

4

5

2

1

3

2

3

Errors with Design 2

4

1

6

8

7

4

2

6

5

2

36.Is this a paired design or a two independent samples design?

37.State the appropriate null and alternative hypotheses for testing the theory that stove design 2 would lead to more errors on average as compared to stove design 1.

38.Calculate the observed test statistic value.

39.Give the corresponding p-value.

40.Using a significance level of α = 0.01, give your decision and state your conclusion in terms of the problem.

41.Report the effect size for this study.

42.According to Cohen’s conventions, approximately how large is this effect?

Questions 43 through 50 are based on the following scenario.

A newspaper claimed that part time students attending the local university are generally older than full time students. The following data on ages of some randomly selected students was collected to assess the validity of this claim.

Ages for full time students

18

19

19

22

20

19

18

19

19

21

Ages for part time students

21

18

26

19

19

22

19

20

43.One assumption required to perform the two independent samples T-test is that the distribution for both populations is normal. Suggest a method for checking this assumption and explain what you would hope to see for the assumption to be valid.

44.What additional assumptions are required to perform the two independent samples T-test on these data? (For questions 39 through 42, assume the assumptions are valid.)

45.State the appropriate null and alternative hypotheses for testing the claim that part time students are older than full time students on average.

46.Calculate the observed test statistic value.

47.Give the corresponding p-value.

48.Using a significance level of α = 0.05, is there significant evidence that part time students are older than full time students on average? Explain.

49.Report the effect size for this study.

50.According to Cohen’s conventions, approximately how large is this effect?