A student was asked to find a $$ 98 \% $$ confidence interval for widget width using data from a random sample of size $$ 7=29 $$ and the student reached the interval of $$ 10.7

Question

A student was asked to find a $$ 98 \% $$ confidence interval for widget width using data from a random sample of size $$ 7=29 $$ and the student reached the interval of $$ 10.7<\beta<27.4 $$ Which of the following is a correct interpretation of this interval? A The wioth of all widgets is between 10.7 and $$ 27.4,98 \% $$ of the time. We know this is true because the mean of our sample is between 10.7 and 27.4 . B. With $$ 98 \% $$ confidence, the wioth of a randomly selected widget will be between 10.7 and 27.4 . C. Whth $$ 98 \% $$ confidence, the mean width of all widgets is between 10.7 and 27.4 . D There is a $$ 98 \% $$ chance that the width of the widget is between 10.7 and 27.4 . E There is a $$ 98 \% $$ chance that the mean of a sample of 29 wiogets will be between 10.7 and 27.4 .

UpStudy AI · Accepted Answer

1. The confidence interval was constructed for the true population mean (the mean width of all widgets), not for the width of individual widgets or a sample's mean.
2. A $$98\%$$ confidence interval means that if we repeated the sampling procedure many times, approximately $$98\%$$ of the constructed intervals would capture the true mean widget width.
3. Thus, the correct interpretation is that we have $$98\%$$ confidence that the interval from $$10.7$$ to $$27.4$$ contains the true mean widget width.

The correct answer is:

C. With $$98 \%$$ confidence, the mean width of all widgets is between $$10.7$$ and $$27.4$$.
With 98% confidence, the mean width of all widgets is between 10.7 and 27.4.

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