Note: Answer all the questions in R$-$Studio. Each question carries

$6.$ Workplace Homicides A sample of six recent years had an average of $573\mathrm{.}8$ workplace homicides per year with a standard deviation of $46\mathrm{.}8.$ Find the $99\%$ confidence interval of the true mean of all workplace homicides per year.

$7.$Days on Dealers' Lots

A researcher wishes to see if the mean number of days that a basic, low$-$price, small automobile sits on a dealer's lot is $29.$ A sample of $30$ automobile dealers has a mean of $30\mathrm{.}1$ days for basic, low$-$price, small automobiles. At $=0\mathrm{.}05,$ test the claim that the mean time is greater than $29$ days. The standard deviation of the population is $3\mathrm{.}8$ days.

$8.$ Cost of College Tuition

A researcher wishes to test the claim that the average cost of tuition and fees at a four year public college is greater than $$5700.$ She selects a random sample of $36$ four$-$year public colleges and finds the mean to be $$5950.$ The population standard deviation is $$659.$ Is there evidence to support the claim at $=0\mathrm{.}05?$ Use the P$-$value method.

$9.$ Hospital Infections

A medical investigation claims that the average number of infections per week at a hospital in southwestern Pennsylvania is $16\mathrm{.}3.$ A random sample of $10$ weeks had a mean number of $17\mathrm{.}7$ infections. The sample standard deviation is $1\mathrm{.}8.$ Is there enough evidence to reject the investigator's claim at $=0\mathrm{.}05?$

$10.$ A researcher wishes to see if there is a relationship between the ages and net worth of the wealthiest people in America. The data for a specific year are shown.

$\backslash$table$[[$Person$,$Age $x,$Net wealth $y($$ billions$)],[$A$,73,16],[$B$,65,26],[$C$,53,50],[$D$,54,21\mathrm{.}5],[$E$,79,40],[$F$,69,16],[$G$,61,19\mathrm{.}6],[$H$,65,19]]$

a$)$ Draw a scatter plot.

b$)$ Compute the correlation coefficient.