Subject	Right hand threads (sec)	Left hand threads (sec)
1	113	137
2	105	105
3	130	133
4	101	108
5	138	115
6	118	170
7	87	103
8	116	145
9	75	78
10	96	107
11	122	84
12	103	148
13	116	147
14	107	87
15	118	166
16	103	146
17	111	123
18	104	135
19	111	112
20	89	93
21	78	76
22	100	116
23	89	78
24	85	101
25	88	123

1. The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25 right handed students to turn a knob with their right hands that moved an indicator by screw action. There were two identical instruments, one with a right-hand thread and the other with a left-hand thread. The table given has the data from the student project.

A. Each student used both instruments, describe how you would use randomization in designing the experiment.

B. The student hoped to show that right handed people find right hand threads easier to use. Carry out a 5% significance test to investigate this claim.

C. Describe a Type I and Type II error in this case and a consequence of both.

D. Calculate and interpret a 90% confidence interval for the mean time advantage of right hand over left hand threads in the setting above.

2. The Acculturation Rating Scale for Mexican Americans (ARSMA) and the Bicultural Inventory (BI) both measure the extent to which Mexican Americans have adopted the Anglo/English culture. These tests were compared by administering both tests to 22 Mexican Americans. Both tests have the same range of scores (1.00 to 5.00) and are scaled to have similar means for the groups used to develop them. There was a high correlation between the two scores, giving evidence that both are measuring the same characteristics. The researchers wanted to know whether the population mean difference in scores for the two tests is 0. The differences in scores (ARSMA - BI) for the 22 participants had a mean of 0.2519 and standard deviation of 0.2767.

A. Carry out a significance test to help answer the researcher's question.

B. Construct and Interpret a 95% confidence interval for the mean difference in scores on the two tests.