Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)} (disregarding order). Let X be the sum of the two balls selected.   Which of the following is the correct distribution for X?

A market researcher is interested in knowing whether placing a product at the checkout of a supermarket, in addition to the shelves, leads to an increase in sales which persists after the product is removed from the checkout. A random selection of pairs of supermarkets is chosen. In one of each of the pairs, the product is placed at the checkout for one week. Sales of the product in all the supermarkets were recorded before and after the placement of the product at the checkout, the change in the differences between each pair were computed, and resulting data were saved in this file. 1. Compute a 90% confidence interval for the expected change in sales due to the product placement. Show your working. 2. Interpret the confidence interval. 3. Do you need to make any assumptions in order for your confidence interval to be valid? x 3.48983 4.94556 4.052113 4.472282 5.540868 4.208772 6.008711 4.498776 3.686976 7.076072 4.076262 5.238185 5.09588 4.880026…

Forty-nine percent of all New York residents prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among New York residents who are Latino, 57% prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Twenty-five percent of all New York residents are Latino. One New York resident is selected at random. For this problem, let: L = the selected New York resident is Latino. N = the selected New York resident prefers life in prison without parole over the death penalty for a person convicted of first degree murder. P(N) = 49 P(L) = .25 P(N | L) = .57 P(L AND N) = Are L and N mutually exclusive events? O There is not enough information to determine whether or not events N andL are mutually exclusive. O Events N and L are mutually exclusive. O Events N and L are not mutually exclusive. P(L OR N) =

- Assume that you randomly pick one of the bowls: X,Y, or Z. You then randomly draw one ball out of the selected bowl and note it's color. The bowls contain the following colored balls:  Bowl X: 2 red, 1 white, and 2 blue  Bowl Y: 4 red, 2 white, and 2 blue  Bowl Z: 3 red, 3 white, and 2 blue  1.) If the ball is blue, what is the probability that it was drawn from bowl X? 2.) If the ball is either blue or white, what is the probability that it was drawn from bowl Y?

A teacher believes that students who study more than four hours for her tests will do better than students who do not study for her tests.  To test this belief, the teacher recruited 16 students and randomly assigned them to two groups:  G1: a group of n1=8 students that studied more than four hours for her test, and G2: a group of n2=8 students that did not study for her test.    The following are the data from G1, who studied more than four hours for the test:   n1=8   M1=85   s1=5 (this is the standard deviation of the sample, dividing the sum of squares by n1)   The following are the data from G2, who did not study for the test:   n2=8   M2=75   s2=4 (this is the standard deviation of the sample, dividing the sum of squares by n2)   Perform a t-test by answering the questions below.  Use an alpha-level of α=.05.    0.  Using formulas from Section 4, compute the estimates of the population variances, est. σ12 and est. σ22 (from s1 and s2 above). 1.  What is the research…

Suppose you are interested in buying a new Lincoln Navigator or Town Car. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on a random selection of these cars of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle. x 32.4 32.9 36.1 44.0 47.8 y 30.4 31.0 32.0 42.1 42.2 (b) Use a 10% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t ? critical t ? (c) Verify that Se ≈ 1.5629, a ≈ 2.5006, and b ≈ 0.8551. Se ? a ? b ? (e) Find a 95% confidence interval for y when x = 42 (thousand dollars). (Use 2 decimal place.) lower limit ? upper limit ? (f) Use a 10% level of significance to test the claim that β > 0. (Use 2 decimal places.) t ? critical t ?

Suppose that a statistics teacher asks his students to each randomly pick one of the numbers 0, 3, 5, 7. His general theory is that the proportion who pick the number 0 will be less than what would be expected from random selection. Use p to represent the population proportion that would pick the number 0. (a) What is the specific value of p that corresponds to true random selection? p = (b) In terms of p, write null and alternative hypotheses for this situation. Ho Ha: P <

Three balls are selected from a bag that contains 3 blue, 2 green, and 5 yellow balls. Here, we define random variables as B = number of blue balls drawn, G = number of green balls drawn, Y = number of yellow balls drawn. Please list the following values:

A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows.  Hours of Training Defects per Countertop 1 5 4 1 7 0 3 3 2 5 2 4 5 1 5 2 1 8 6 2 Copy Data The estimated regression line and the standard error are given.  Defects per Countertop=6.717822−1.004950(Hours of Training)se=1.229787se=1.229787  Suppose a new employee has had 5 hours of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.

8 For this problem, assume there are 3 grey females, 4 grey males, 2 white females, and 3 white males. As in the book, the biologist selects two mice randomly. (1) What is the probability of selecting two males given that both are grey? (2) What is the probability of selecting 1 mouse of each gender given that both are grey?