Mathematics, 07.04.2020 01:35 nancyrj3824
Confidence Interval Mistakes and Misunderstandings—Suppose that 500 randomly selected recent graduates of a university were asked to rate the school’s academic advising services on a scale from 1 to 10. The sample mean rating was found to be 8.6. Assume that the population standard deviation is known to be 2.2
A.) Someone computes the 95% confidence interval for the average satisfaction score as 8.6 ± 1.96(2.2). What is the mistake of this student?
B.) After correcting the mistake in part (A), the student states "I am 95% confident that the sample mean rating falls between 8.4 and 8.8." What is wrong with this statement?
C.) The student quickly realizes the mistake made in part (B) and now says "The probability that the true mean rating is between 8.4 and 8.8 is 95%." What misinterpretation is the student making now?
D.) Finally, to defend the use of the Normal distribution to calculate the confidence interval the student says, "Because the sample size is quite large, the population of alumni ratings will be approximately Normal." Correct this misunderstanding.
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Confidence Interval Mistakes and Misunderstandings—Suppose that 500 randomly selected recent gradu...
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