### Statistical Analysis of Heights #### Problem Statement: The distribution of heights of young women aged 18 to 24 is approximately normal with a mean \(\mu = 64.5\) inches and a standard deviation \(\sigma = 2.5\) inches. The table contains the heights (in inches) of a random sample of 93 female undergraduate students at the University of California at Irvine. We are tasked with determining if the mean height of all female undergraduate students at UC Irvine is different from the mean height of 64.5 inches for all young women in the US. #### Data: The table below represents the heights of the selected sample: \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline 54 & 54 & 56 & 57 & 58 & 58 & 59 & 60 & 60 & 61 \\ \hline 60 & 60 & 61 & 61 & 61 & 61 & 61 & 61 & 61 & 62 \\ \hline 61 & 62 & 62 & 62 & 62 & 62 & 62 & 62 & 63 & 63 \\ \hline 62 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 64 & 64 \\ \hline 64 & 64 & 64 & 64 & 64 & 64 & 64 & 64 & 64 & 64 \\ \hline 64 & 65 & 65 & 65 & 65 & 65 & 66 & 66 & 66 & 66 \\ \hline 68 & 68 & 70 & & & & & & & \\ \hline \end{array} \] #### Questions: (a) **Identify what the statistician is trying to find (confidence interval or hypothesis test).** The statistician is trying to perform a **hypothesis test** to see if the sample mean significantly differs from the population mean of 64.5 inches. (b) **Which procedure (z or t) he/she/they should use to find it.** Since the population standard deviation is known and the sample size is large (n = 93), a **z-test** should be used

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