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Solved: Exercises 55 and 56 refer to the following setting. Coaching companies claim
Chapter 10, Problem 56(choose chapter or problem)
Exercises 55 and 56 refer to the following setting. Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached.41 Starting with their Verbal scores on the first and second tries, we have these summary statistics:Coaching and SAT scores What we really want toknow is whether coached students improve morethan uncoached students, and whether any advantageis large enough to be worth paying for. Use theinformation above to answer these questions:(a) How much more do coached students gain on the average?Construct and interpret a 99% confidence interval.(b) Does the interval in part (a) give convincing evidencethat coached students gain more, on average,than uncoached students? Explain.(c) Based on your work, what is your opinion: do youthink coaching courses are worth paying for?
Questions & Answers
QUESTION:
Exercises 55 and 56 refer to the following setting. Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached.41 Starting with their Verbal scores on the first and second tries, we have these summary statistics:Coaching and SAT scores What we really want toknow is whether coached students improve morethan uncoached students, and whether any advantageis large enough to be worth paying for. Use theinformation above to answer these questions:(a) How much more do coached students gain on the average?Construct and interpret a 99% confidence interval.(b) Does the interval in part (a) give convincing evidencethat coached students gain more, on average,than uncoached students? Explain.(c) Based on your work, what is your opinion: do youthink coaching courses are worth paying for?
ANSWER:Step 1 of 4
(a)
Given:
The three conditions for determine a confidence interval for the difference in population means are: Random, Independent (10\% condition), Normal/Large sample.
Random: Satisfied, because the samples are separate sample samples.
Independent: Satisfied, because the sample of 427 coached students is less than of the population of coached students and the sample of 2733 uncoached students is less than of the population of all uncoached students (assuming that there are at least 4270 coached students and at least 27330 uncoached students).
Normal/Large sample: Satisfied, because both samples are large (as the sample size of 427 and the sample size of 2733 are both larger than 30).
Since all conditions are satisfied, it is appropriate to determine a confidence interval for the mean difference