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Development officials in a large town in India are planning a new public housing development. To understand what home sizes are currently available to residents, they asked $100$ randomly selected homeowners for the area of their homes in square meters. The officials found a $99\%$ confidence interval of for the mean area of homes in the town. $\newline$ Is the following conclusion valid? $\newline$ If $100$ more samples are taken (with elements chosen randomly and independently), it is expected that the mean area of homes in the town would be in $99$ of the computed $99\%$ confidence intervals. $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$

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Interpret confidence intervals for population means

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Q. Development officials in a large town in India are planning a new public housing development. To understand what home sizes are currently available to residents, they asked

100

randomly selected homeowners for the area of their homes in square meters. The officials found a

99\%

confidence interval of for the mean area of homes in the town.

\newline

Is the following conclusion valid?

\newline

If

100

more samples are taken (with elements chosen randomly and independently), it is expected that the mean area of homes in the town would be in

99

of the computed

99\%

confidence intervals.

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Definition of $99$ % Confidence Interval: The concept of a $99\%$ confidence interval means that if we were to take many samples and build a confidence interval from each of them, $99\%$ of these intervals would contain the true mean.
Expectation from $100$ Samples: So, if $100$ more samples are taken, we expect that approximately $99$ of those $100$ confidence intervals will contain the true mean area of homes.
Validity of Conclusion: Therefore, the conclusion given in the question is valid based on the definition of a confidence interval.

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