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 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?

Determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.

If $\overline{x}$ is the mean of a large $(n \gt 30)$ simple random sample from a population with mean $\mu$ and standard deviation $\sigma$, then $\overline{x}$ is approximately normal with $\sigma_{\overline{x}} = \dfrac{\sigma}{\sqrt{n}}$ .

Suppose you plan to take a random sample of 1,000 Hispanics in the United States. Assume that the distribution of origin has not changed since 2010.

a. What proportion of Hispanics in the United States in 2010 were of Mexican origin? What is the expected number of Hispanics in your sample who will be of Mexican origin?

b. What proportion of Hispanics in the United States in 2010 were of Puerto Rican origin? What is the expected number of Hispanics in your sample who will be of Puerto Rican origin?

c. Now suppose that you take a random sample of 1,000 Hispanics from your state and find 521 Hispanics of Mexican origin. A friend takes a second random sample of 1,500 Hispanics from your state and finds 847 of Mexican origin. What is the best estimate of the proportion of Hispanics in your state who are of Mexican origin?

d. Suppose you plan to take yet another random sample from your state, this time of 500 Hispanics. Based on your work in Part c, what is the best estimate of the expected number of Hispanics of Mexican origin you will find in this sample?

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:

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:

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

Completing each sentence with a word or phrase.

A _______________ is a master plan for achieving a goal.

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, B and C are three circles of unit radius with centres in the x y-plane at (1,2),(2.5,1.5) and (2,3), respectively. Devise a hit or miss Monte Carlo calculation to determine the size of the area that lies outside C but inside $A$ and $B$, as well as inside the square centred on $(2,2.5)$, that has sides of length 2 parallel to the coordinate axes. You should choose your sampling region so as to make the estimation as efficient as possible. Take the random number distribution to be uniform on $(0,1)$ and determine the inequalities that have to be tested using the random numbers chosen.

In 1970, 59% of college freshmen thought that capital punishment should be abolished; by 2005, the percentage had dropped to 35%. Is the difference real, or can it be explained by chance? You may assume that the percentages are based on two independent simple random samples, each of size 1,000.

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?

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.

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.