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Fifty students are enrolled in an Economics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90.
a. Calculate the estimate of the standard error of the mean.
b. What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why.
c. Assume the assumption of Part b is met. Provide a 90% confidence interval for the mean grade of all the students in the class.
d. If there were 200 students in the class, what would be the 90% confidence interval for the mean grade of all the students in the class?
What happens to the confidence interval when we go from a 95% confidence level to a 99% confidence level? Is this desirable? When would we want to use a 99% confidence interval?
If the class does well on an exam, then the next exam is equally likely to be any of the three types. If the class does badly, then the next exam is always type 1. What proportion of exams are type 1, 2, and 3?
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A few random results for you to ponder...do the results justify the conclusions? Why or why not? Give a reason why the conclusions don't necessarily follow from the statement.
The American Bar Association conducted a survey in 1986 showed that the average income of lawyers in 1986 was $ 120,000. An investigator took a sample of 64 lawyers in 1990, produced a median income of $ 140,000 with a standard deviation of $ 24.5..
Determine the frequencies expected if the two variables, status regarding lab techniques course and laboratory performance, are independent.
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