Math / Data & Statistics

QuestionDance Company Students The number of students who belong to the dance company at each of several randomly selected small universities is shown below. Round sample statistics and final answers to at least one decimal place. \begin{tabular}{llllllll} 27 & 21 & 47 & 21 & 32 & 32 & 35 & 29 \\ 35 & 26 & 35 & 30 & 21 & 21 & 32 & 25 \end{tabular}
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Estimate the true population mean size of a university dance company with $95 \%$ confidence. Assume the variable is normally distributed.

Studdy Solution
Calculate the confidence interval for the population mean:
The margin of error (ME) is:
$ME = t^* \times SE = 2.131 \times 1.325 \approx 2.82$
The confidence interval is:
$\bar{x} \pm ME = 26.5 \pm 2.82$
$= (23.68, 29.32)$
The 95% confidence interval for the true population mean size of a university dance company is:
$\boxed{(23.7, 29.3)}$

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