The Acculturation Rating Scale for Mexican Americans (ARSMA) is a test that measures the extent to which Mexican Americans have adopted Anglo/English culture. A similar test, the Bicultural Inventory (BI), attempts to do the same thing. To compare the tests, researchers administer 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 scores for the two tests were the same. The differences in scores (ARSMA - BI) for the 22 subjects had x = 0.2519 and s = 0.2767.
(a) Describe briefly how the administration of the two tests to the subjects should be conducted, including randomization.
(b) Carry out a significance test for the hypothesis that the two tests have the same population mean. Give the P-value and state your conclusions.
(c) Give a 95% confidence interval for the difference between the two population mean scores.