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

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

Listed below are annual salaries (in thousands of dollars) for a simple random sample of NCAA Division 1-A head football coaches (based on data from the New York Times).

$$\begin{array}{llllllllll} 235 & 159 & 492 & 530 & 138 & 125 & 128 & 900 & 360 & 212 \end{array}$$

a. Find the mean $\bar{x}$ and express the result in dollars instead of thousands of dollars.

An ecologist wishes to mark off a circular sampling region having a radius $10{m}$. However, the radius of the resulting region is actually a random variable $R$ with pdf

$$f(r)=\left\{\begin{array}{cl} \frac{3}{4}\left[1-(10-r)^2\right] & 9 \leq r \leq 11 \\ 0 & \text { otherwise } \end{array}\right.$$

What is the expected area of the resulting circular region?

Work in a group of four to plan your ten-year class reunion in Punta Cana, Dominican Republic. Plan how long the reunion will be, what activities people can participate in, and what food will be served. Create an invitation and present it to the class. After looking at all of the invitations, vote for the plan that you want to use for your class reunion.

Compare your answers in the previous exercise. How much influence does the sampling method have on your chances of winning a prize?

Test the given claim. Assume that both samples are independent simple random samples from populations having normal distributions.

A random sample of 13 four-cylinder cars is obtained, and the braking distances are measured and found to have a mean of $137.5 \mathrm{ft}$ and a standard deviation of $5.8 \mathrm{ft}$. A random sample of 12 six-cylinder cars is obtained and the braking distances have a mean of $136.3 \mathrm{ft}$ and a standard deviation of $9.7 \mathrm{ft}$. Use a $0.05$ significance level to test the claim that braking distances of four-cylinder cars and braking distances of six-cylinder cars have the same standard deviation.

Identify National Guard, attorney general, secretary of state, Missouri Plan.

Why do you think many people considered Columbus' plan to be controversial?

Listed below are annual salaries (in thousands of dollars) for a simple random sample of NCAA Division 1-A head football coaches (based on data from the New York Times).

$$\begin{array}{llllllllll} 235 & 159 & 492 & 530 & 138 & 125 & 128 & 900 & 360 & 212 \end{array}$$

d. Find the variance $s^2$ and express the result in appropriate units.

The number of dirt specks on a randomly selected square yard of polyethylene film of a certain type has a Poisson distribution with a mean value of 2 specks per square yard. Consider a random sample of $n=5$ film specimens, each having area 1 square yard, and let $\bar{X}$ be the resulting sample mean number of dirt specks. Obtain the first 21 probabilities in the $\bar{X}$ sampling distribution.

Given a simple random sample of 20 speeds of cars on Highway 405 in California, you want to test the claim that the sample values are from a population with a mean greater than the posted speed limit of $65 \mathrm{mi} / \mathrm{h}$. Is it necessary to determine whether the sample is from a normally distributed population? If so, what methods can be used to make that determination?

You must choose an SRS of 10 of the 440 retail outlets in New York that sell your company's products. How would you label this population to select a simple random sample?

(a) 001, 002, 003, . . . , 439, 440

(b) 000, 001, 002, . . . , 439, 440

(c) 1, 2, . . . ,439, 440

Completing each sentence with a word or phrase.

A _______________ is a master plan for achieving a goal.

Based on past experience, $20 \%$ of the contacts made by a firm's sales representatives result in a sale being made. Charlie has contacted 100 potential customers but has made only 10 sales. Assume that Charlie's contacts represent a simple random sample of those who could have been called upon. Given this information: