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?

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

The sampling distribution for the goodness of fit test is the

A. Poisson distribution
B. t distribution
C. normal distribution
D. chi-square distribution

Completing each sentence with a word or phrase.

A _______________ is a master plan for achieving a goal.

Monthly Sales Data. A simple random sample of 5 months of sales data provided the following information:

$$\begin{array}{lrrrrr}\text { Month: } & 1 & 2 & 3 & 4 & 5 \\ \text { Units Sold: } & 94 & 100 & 85 & 94 & 92\end{array}$$

a. Develop a point estimate of the population mean number of units sold per month.

The earlier exercise presents the results of a poll evaluating support for the health care public option plan in 2009. $70 \%$ of 819 Democrats and $42 \%$ of 783 Independents support the public option.

(a) Calculate a $95 \%$ confidence interval for the difference between $\left(p_D-p_I\right)$ and interpret it in this context. We have already checked conditions for you.

(b) True or false: If we had picked a random Democrat and a random Independent at the time of this poll, it is more likely that the Democrat would support the public option than the Independent.

A coach must select two players to serve as captains. He wants to randomly select two players to be the captains. Obtain a simple random sample of size 2 from the following list: Mady, Breanne, Evin, Tori, Emily, Clair, Caty, Jory, Payton, Jordyn. Write a short description of the process you used to generate your sample.

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.

The solid represented by the Mat Plan is built and glued together. The solid is dipped in red paint and then left to dry. Once dried, the cubes are broken apart and each cube is dropped into a bag. If you are going to reach into the bag and pull out a cube at random, what is the probability that the cube has at least one red face?

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

Quieres participar en un concurso literario para escritores jóvenes. Para la primera etapa del concurso, hay que entregar un plan del cuento. Usando el plan en la página 119 como modelo, prepara un plan para tu propio cuento. ¿Qué información vas a incluir alli y cómo piensas organizar el plan?

The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 50 Buffalo residents the mean is $22.5$ miles a day and the standard deviation is $8.4$ miles a day, and for an independent simple random sample of 40 Boston residents the mean is $18.6$ miles a day and the standard deviation is $7.4$ miles a day.

What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day?

What is the $95 \%$ confidence interval for the difference between the two population means?

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:

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

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.