The Acculteration Rating Scale for Mexican Americans ARSMA m

The Acculteration Rating Scale for Mexican Americans (ARSMA) measures the extent to which Mexican Americans have adopted Anglo/English culture. During the development of ARSMA, the test was given to a group of 17 Mexicans. Their scores, from a possible range of 1.00 to 5.00, had x=1.67 and s=0.25. Because low scores should indicate a Mexican cultural orientation, these results helped to establish the validity of the test.

A) Give a 95% confidence interval for the mean ARSMA score of Mexicans.

B) What assumptions does your confidence interval require? Which of these assumptions is most important in this case?

Solution

A) Give a 95% confidence interval for the mean ARSMA score of Mexicans.

The degree of freedom =n-1=17-1=16

Given a=1-0.95=0.05, t(0.025, df=16) =2.12 (from student t table)

So the lower bound is

xbar - t*s/vn =1.67 -2.12*0.25/sqrt(17) =1.541456

So the upper bound is

xbar +t*s/vn=1.67 +2.12*0.25/sqrt(17)=1.798544

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B) What assumptions does your confidence interval require? Which of these assumptions is most important in this case?

We need to assume that the population follows normal distribution and unknown population variance.

Normal distributin assumption is most important in this case because we need it to calculate the confidence interval.