Math / Data & Statistics

QuestionNumber of Farms A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with $99 \%$ confidence. Assume $\sigma=31$ . Round intermediate and final answers to one decimal place. Assume the population is normally distributed. $\begin{array}{ccccccccccc} 4 & 64 & 33 & 54 & 95 & 47 & 50 & 40 & 109 & 78 & 6 \\ 52 & 21 & 15 & 7 & 68 & 16 & 48 & 79 & 44 & & \end{array}$ Send data to Excel $\square<\mu<\square$

Studdy Solution
Construct the confidence interval for the mean.
The confidence interval is given by:
$\bar{x} - ME < \mu < \bar{x} + ME$
Substitute the values:
$49.0 - 17.9 < \mu < 49.0 + 17.9$
$31.1 < \mu < 66.9$
The 99% confidence interval for the mean number of farms per state is:
$\boxed{31.1 < \mu < 66.9}$

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