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IQ comparison of older vs. younger workers. The Age
Chapter 6, Problem 125SE(choose chapter or problem)
IQ comparison of older vs. younger workers. The Age Discrimination in Employment Act (ADEA) 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 want to hire and train workers who are very close to retirement. They also argue that people’s abilities tend to deteriorate with age. Do 25-year-olds score significantly higher than 60-year-olds on the Wechsler Adult Intelligence Scale, the most popular IQ test? The data in the next table are raw test scores (i.e., not the familiar normalized IQ scores) for a sample of thirty-six 25-year-olds and thirty-six 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.
Questions & Answers
QUESTION:
IQ comparison of older vs. younger workers. The Age Discrimination in Employment Act (ADEA) 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 want to hire and train workers who are very close to retirement. They also argue that people’s abilities tend to deteriorate with age. Do 25-year-olds score significantly higher than 60-year-olds on the Wechsler Adult Intelligence Scale, the most popular IQ test? The data in the next table are raw test scores (i.e., not the familiar normalized IQ scores) for a sample of thirty-six 25-year-olds and thirty-six 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.
ANSWER:Solution
Step 1 of 3
a) We have to estimate 99% confidence interval for mean for the scores of 25 years old
For 99% confidence
From the tables the critical value of z is
Enter the given data in Ms-Excel
Get the mean and standard deviation values from the excel for 25 years old
Now mean (
=66.83
Standard deviation (s)=
=14.36
Now the 99% confidence interval for mean is
=
=66.836.175
=(60.655, 73.005)
Hence the 99% confidence interval for mean for the scores of 25 years old is
(60.655, 73.005)