(Solved): An arborist recorded the diameter of seven randomly selected mature white oak trees ( 64.033.445.8, ...

An arborist recorded the diameter of seven randomly selected mature white oak trees ( $\mathrm{64.033.445.8},56.0$, $51.5,\mathrm{29.263.7}$ ) and wanted to know if the trees were growing as expected. Specifically, he wanted to know if the tree's diameter were an average of $40\mathrm{cm}1$ meter above the base. He wants you to perform a statistical test to test whether the average diameter of the trees is $40\mathrm{cm}$. You may assume the data are normally distributed. Use $a=0.05$. a. State the statistical assumptions the data need to meet to ensure reliable results. b. State the null and alternative hypothesis for this problem, i.e., $H_0$ and $H_{?}$. c. 1. Compute the test statistic by hand. ii. Confirm your computation of the test statistic using either prop.test() or t.test() command. d. Report the $p$-values from parts $I$, and ii. Interpret. That is, how likely is the result if $H_0$ is true. Is the test statistic usual or unusual? e. State your conclusion about $40\mathrm{cm}$ using words that the arborist can understand (do not assume they know statistics). f. What conclusions can you make about the $40\mathrm{cm}$ tree diameter based on the hypothesis test and confidence interval computed in HW5 Problem 3 ? g. Do your answers from parts e. and $f$, agree? Explain.|