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Topic: Understanding Confidence Intervals. Please comment.
Replies: 1   Last Post: Nov 9, 2009 3:20 PM

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 Bacle Posts: 818 From: NYC Registered: 6/21/09
Posted: Nov 9, 2009 2:30 AM

Could someone please tell me if I am understanding confidence intervals correctly.?. Here is a problem I
am trying to answer.( I will mark my answers with a ------- to make it easier to recognize. Please feel free to check just one-or-two of the answers if this seems too long). I would appreciate your comments:

Here is the problem:

Teachers
Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What's wrong with the others?

t-Interval for m: with 90.00% Confidence, 38944 < m(TchPay) < 42893

a)If we took many random samples of Nevada teachers, about 9 out of 10 of them would produce this confidence interval.

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a)False: the confidence interval would depend on the value of sampling mean. Since we are using t-intervals, we must be using the sample error, which makes intervals even more variable than if we knew the true pop. standard deviation.

All we can say is that there is a 95% probability that
the true average salary lies in a 95% confidence interval, whatever interval we construct.

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b)If we took many random samples of Nevada teachers, about 9 out of 10 of them would produce a confidence interval that contained the mean salary of all Nevada teachers.

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True, if we constructed 95% confidence t-intervals with the sampling data given.

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c)About 9 out of 10 Nevada teachers earn between \$38,944 and \$42,893.

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False. The confidence interval is about the true population mean, about the probability that the true mean lies in the interval, not about the probability that a teacher earns an amount in this range.

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d)About 9 out of 10 of the teachers surveyed earn between \$38,944 and \$42,893.
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False.

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d)We are 90% confident that the average teacher salary in the United States is between \$38,944 and \$42,893.

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d)True. This is the actual meaning of a confidence interval.