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Residents of a small fishing village are gathering the largest clams they can find for an upcoming clam festival. To investigate the environmental impact of this event, activists measured the widths of $175$ randomly selected clams from a local beach (in centimeters). From their measurements, the activists calculated a $95\%$ confidence interval of for the mean width of the clams from this beach. $\newline$ Is the following conclusion valid? $\newline$ There is a $95\%$ chance that the mean width of all clams from this beach is in the interval . $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Interpret confidence intervals for population means

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Q. Residents of a small fishing village are gathering the largest clams they can find for an upcoming clam festival. To investigate the environmental impact of this event, activists measured the widths of

175

randomly selected clams from a local beach (in centimeters). From their measurements, the activists calculated a

95\%

confidence interval of for the mean width of the clams from this beach.

\newline

Is the following conclusion valid?

\newline

There is a

95\%

chance that the mean width of all clams from this beach is in the interval .

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Understand Confidence Interval Definition: To answer the question, we need to understand what a $95\%$ confidence interval represents. A $95\%$ confidence interval means that if we were to take many random samples and calculate the confidence interval for each sample, $95\%$ of those intervals would contain the true mean.
Clarify Common Misunderstanding: The conclusion that there is a $95\%$ chance that the mean width of all clams from this beach is in the interval is a common misunderstanding. The correct interpretation is that we are $95\%$ confident that the interval contains the true mean width of the clams, not that there is a $95\%$ chance that any given interval contains the true mean.
Answer the Question: Therefore, the answer to the question is (B) no, because the statement misinterprets the meaning of a confidence interval.

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