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The superintendent of Morristown School District is concerned about the study habits of students in the district. He had guidance counselors throughout the city ask $100$ randomly chosen students how many hours they study each day. The superintendent computed a $95\%$ confidence interval for the mean number of hours students in Morristown study each day. $\newline$ Is the following conclusion valid? $\newline$ If Sam takes more same-sized samples, then $95\%$ of the students in each sample will study between $2.9$ and $3.3$ hours each day. $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$

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Interpret confidence intervals for population means

Full solution

Q. The superintendent of Morristown School District is concerned about the study habits of students in the district. He had guidance counselors throughout the city ask

100

randomly chosen students how many hours they study each day. The superintendent computed a

95\%

confidence interval for the mean number of hours students in Morristown study each day.

\newline

Is the following conclusion valid?

\newline

If Sam takes more same-sized samples, then

95\%

of the students in each sample will study between

2.9

and

3.3

hours each day.

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Confidence Interval Explanation: A $95\%$ confidence interval for the mean is about where we expect the true mean of the population to fall, not individual observations.
Superintendent's Incorrect Conclusion: The superintendent's conclusion is incorrect because the confidence interval applies to the mean of the sample means, not the individual study times of students in each sample.

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