Question

Given the following observations in a simple random sample from a population that is approximately normally distributed, construct and interpret the 95%95 \% and 99%99 \% confidence intervals for the mean:

6634595651453858525250344261534857475054\begin{array}{llllllllll}66 & 34 & 59 & 56 & 51 & 45 & 38 & 58 & 52 & 52 \\ 50 & 34 & 42 & 61 & 53 & 48 & 57 & 47 & 50 & 54\end{array}

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Let's define the following set of observations in 2020 randomly selected samples from a normally distributed population: x={66,34,59,56,51,45,38,58,52,52,50,34,42,61,53,48,57,47,50,54}x=\{66, 34, 59, 56, 51, 45, 38, 58, 52, 52, 50, 34, 42, 61, 53, 48, 57, 47, 50, 54\}

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