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# Confidence Interval using the t or z test with assumptions

IQ comparison of older vs. younger workers.

the 1967 Age Discrimination in Employment Act made it illegal to discriminate against workers 40 years of age and older. Opponents of the law argue that there are sound economic reasons why employers would not wan tto hire and train workers who are very close to retirement. They also argue that people's abilities begin to deteriorate with age. In fact, Forbe's (Dec 13, 1999) reported that 25-year-olds did significantly better than 60 year olds on the Wechsler Adult Intelligence Scale, the most populat IQ test. The following data are raw test scores (ie, not the familiarized IQ scores) for a sample of thirty six 25-year-olds and 36 60-year-olds:

a) Estimate the mean raw test score for all 25-year-olds using a 99% confidence interval. Give a practical interpretation of the confidence interval.

b) What assumption(s) must hold for the method of estimation used in part a to be appropriate?

c) Find a 95% confidence interval for the mean raw score of all 60-year-olds and interpret your result

Data:

Scores of 25-year-olds: 54; 61; 80; 92; 41; 63; 59; 68; 66; 76; 82; 80; 82; 47; 81; 77; 88; 94; 49; 86; 55; 82; 45; 51; 70; 72; 63; 50; 52; 67; 75; 60; 58; 49; 63; 68

Scores of 60-year-olds: 42; 54; 38; 22; 58; 37; 60; 49; 51; 60; 45; 42; 73; 28; 65; 65; 60; 34; 34; 33; 40; 28; 36; 60; 45; 61; 47; 30; 45; 45; 45; 37; 27; 40; 37; 58

#### Solution Summary

This solution is comprised of a detailed explanation of Confidence Interval with the help of excel. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of Confidence Interval using the t or z test after discussing the assumptions of the test.

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