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A council member in a Canadian town wants to know if registered voters would support a proposal to raise the speed limit on a local road. Her staff polled $150$ randomly selected voters and asked them to estimate the safest maximum speed on the road. From the survey results, the staff calculated a $99\%$ confidence interval of for the mean estimate among registered voters. $\newline$ Is the following conclusion valid? $\newline$ If the staff conduct another survey, there is a $99\%$ chance that the mean estimate among registered voters will be in the new survey's $99\%$ confidence interval. $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$

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Interpret confidence intervals for population means

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Q. A council member in a Canadian town wants to know if registered voters would support a proposal to raise the speed limit on a local road. Her staff polled

150

randomly selected voters and asked them to estimate the safest maximum speed on the road. From the survey results, the staff calculated a

99\%

confidence interval of for the mean estimate among registered voters.

\newline

Is the following conclusion valid?

\newline

If the staff conduct another survey, there is a

99\%

chance that the mean estimate among registered voters will be in the new survey's

99\%

confidence interval.

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Confidence Interval Definition: The confidence interval gives us the range in which we expect the true mean to fall, given a certain level of confidence.
Specific $99\%$ Interval: The $99\%$ confidence interval from the first survey is based on the data from that specific sample.
Impact of New Survey: If a new survey is conducted, it will have a different sample of voters, which could lead to a different $99\%$ confidence interval.
Correct Interpretation: The conclusion that there is a $99\%$ chance that the mean estimate will be in the new survey's $99\%$ confidence interval is incorrect. The correct interpretation is that we can be $99\%$ confident that the true mean lies within the calculated interval, not that future samples will fall within this interval.

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