I want question 8 answered question 7 is posted because data from that question is required to answer 8

7. The following is the joint probability distribution of number of car crashes (C) and car make (M). C = 0 C = 1 C = 2 C = 3 C = 4 TOYOTA (M = 0) 0.35 0.065 0.05 0.025 0.01 OTHER (M = 1) 0.45 0.035 0.01 0.005 0.00 A. Report the marginal probability distribution for C B. What is the average number of car crash? C. What is the variance of the number of crashes? D. Calculate σCM and ρCM.

8. Suppose car manufacturers are penalized (P) on the basis of the following formula P = 60,000 + 6C – 2M Using your answers for Question 7, calculate the following A. The average penalty (P) B. The variance of penalty (P)

A statewide census examined the number of beds in households and reported a mean (μ) of 2.25 beds and standard deviation (σ) of 1.9 beds per household. But, since I live in a neighborhood with larger families, I have a hunch that the average number of beds in households will be higher in my neighborhood. To test this idea, I randomly picked 25 families in my neighborhood and surveyed them on the number of beds in their home. I would like to perform a Z test to see if the average number of beds in households in my neighborhood is significantly higher than the statewide average. The significance level for my Z test was set at α = .10.

a) What is the dependent variable in this study? b) What should be my null and alternative hypotheses? State each hypothesis using both words and statistical notation. Hint: I am interested in the idea of my neighbors having more beds per household than the state average, so the hypotheses would be directional. c) Calculate the sample mean. d) Calculate standard error (SE, which is the standard deviation of the sampling distribution) e) Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) f) Specify whether the hypothesis test should be a two-tailed or a one-tailed test, and explain the rationale for the choice. g) Determine the critical value for Z h) Compare obtained Z and critical Z and then make a decision about the result of the hypothesis test: Explicitly state “reject” or “fail to reject” the null hypothesis i) Write a 1-2 sentence conclusion interpreting the results (you can simply restate the accepted hypothesis or explain it in another way) j) Calculate the raw and standardized effect sizes k) If the test was done with α level of .05, using the same directional hypotheses, what would be the critical Z value from the Z table? What would be the result of the hypothesis test (in terms of rejecting or failing to reject the null hypothesis)? l) Compare the hypothesis tests result when α = .05 and when α = .10. Were the results the same? Why or why not?

Use the given values of

n=2112

and

p=3/4

to find the maximum value that is significantly​ low,

muμminus−2sigmaσ​,

and the minimum value that is significantly​ high,

muμplus+2sigmaσ.

Round your answer to the nearest hundredth unless otherwise noted.

In the book Analysis of Longitudinal Data, 2nd ed., (2002, Oxford University Press), by Diggle, Heagerty, Liang,and Zeger, the authors analyzed the effects of three diets on the protein content of cow’s milk. The data shown here were collected after one week and include 25 cows on the barley diet and 27 cows each on the other two diets:

(a) What is the value of LSD for Barley+Lupins diet and Lupins diet? Use α=0.05.
Round your answer to three decimal places (e.g. 98.765).

(c) What is the absolute value of difference between mean protein content after Barley+Lupins diet and Lupins diet?
Round your answer to three decimal places (e.g. 98.765).

(d) Estimate the standard error for comparing the means using the graphical method. Use minimum sample size.
Round your answer to three decimal places (e.g. 98.765).

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Enter a number. Round your answer to four decimal places.) The area to the left of z = 0.42 is ?

We always seem to be focused on using statistics in Business decisions. Please think of some ways you can use statistics in your own decision making. For example, when we go on vacation as a family, we choose between many different types of travel. Using statistical analysis, I am able to come up with different pricing options.

A restaurant uses comment cards to get feedback from its customers about newly added items to the menu. It recently introduced homemade organic veggie burgers. Customers who tried the new burger were asked if they would order it again. The data are summarized in the table below. Which of the following would be an appropriate method for displaying the data shown in the​ table?

Response Frequency Definitely would 10 Most likely would 40 Maybe 12 Definitely would not 3

Possible Answers (please choose one)
Frequency Histogram
Box & Whisker Plot
Stem & Leaf Display
Relative Frequency Bar Chart

A business researcher conducted a survey of 500 women to determine preferences for types of automobiles. The types are shown below along with the number of women who prefer each type. Which of the following charts would be appropriate for displaying these​ data?

Type of Automobile Females Sedan 155 SUV 112 Van 125 Sports cars 55 Convertible 28 Other 25

Possible Answers (please choose one)
Histogram
Box & Whisker Plot
Stem & Leaf Display
Pie Chart

For the following situations, please write out null and alternative hypotheses.

a. Assuming m = 100, do children who watch more than three hours of TV per day have significantly lower IQs?

b. Assuming m = 100, a cognitive psychologist would like to know if the IQs of children who play outside at least three days a week are different from that of the population.

c. Assuming m = 50, write out the null and a non-directional alternative hypothesis.

identify (but don't collect) a type of dataset that might be normally distributed, and then answer the following questions:

• What is brief description of the data?
• Is the data normally distributed? Specifically, why is the data not uniformly distributed, or distributed in some other way?
• Normal data is clustered around the mean; what might cause the data you identified to have a different shape and not be clustered around the mean?

A simple random sample of 60 items from a population of with α=8 resulted in a sample mean of 35.

A. Provide a 90% confidence interval for the population mean.

B. Provide a 95% confidence interval for the population mean.

C. Provide a 99% confidence interval for the population mean.

Round to 2 decimal places if necessary.

The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these​ data, the​ least-squares regression line is ModifyingAbove y with -0.006x + 42.216. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon.

​(a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on Rsquared​? ​

(b) Is the point corresponding to the twelfth car​ influential? Is it an​ outlier?

Car, Weight (pounds) x, Miles per Gallon y
1 3766 20
2 3989 21
3 3532 20
4 3170 22
5 2575 28
6 3735 20
7 2605 27
8 3772 18
9 3310 19
10 2993 26
11 2755 25

A point is chosen uniformly at random from a disk of radius 1, centered at the origin. Let R be the distance of the point from the origin, and Θ the angle, measured in radians, counterclockwise with respect to the x-axis, of the line connecting the origin to the point.

1. Find the joint distribution function of (R,Θ); i.e. find F(r,θ) = P(R ≤ r, Θ ≤ θ).

2. Are R and Θ independent? Explain your answer.

In the Blade Runner universe, replicants are bioengineered androids that are virtually identical to humans. The “Voight-Kampff” test is designed to distinguish replicants from humans based on their emotional response to test questions. The test designers guarantee an accuracy rate of 90%. In other words, they guarantee that if a replicant is subjected to the test, then the test will correctly label them as a replicant with probability q = 90%. With the remaining probability, the test incorrectly labels the replicant as a human. Similarly, if a human is subjected to the test, then they will be correctly labelled as human with probability q = 90%, and with the remaining probability they will be incorrectly labelled as a replicant. A subject, Leon, is suspected to be a replicant. Your prior probability that Leon is a replicant equals p = 75% and with the remaining probability 1 − p = 25% you suspect Leon is a human. (a) What is the probability that if Leon takes the Voight-Kampff test, the test will label him as a replicant? (b) Leon is subjected to the Voight-Kampff test, and the test labels Leon as a replicant. What is your posterior probability about whether Leon is a replicant or not? (c) Another subject, Deckard, is also suspected to be a replicant, and your prior probability is that Deckard is a replicant with probability p1 = 10% and human with probability 1 − p1 = 90%. Deckard takes the test, and is labelled as a human. What is your posterior probability about Deckard?

. Arsalaan A., a well-known financial analyst, selected 50 consecutive years of U.S. financial markets data at random. For 11 of the years, the rate of return for the Dow Jones Industrial Average [DJIA] exceeded the rates of return for both the S&P 500 Index and the NASDAQ Composite Index. For 8 of the years, the rate of return for the DJIA trailed the rates of return for both the S&P 500 and the NASDAQ. For 21 of the years, the rate of return for the DJIA trailed the rate of return for the S&P 500. Over the 50 years,

a. determine the probability the rate of return for the DJIA trailed the rate of return for the NASDAQ.
b. determine the probability the rate of return for the DJIA trailed the rate of return for at least one of the other two Indexes.
c. determine the probability the rate of return for the DJIA trailed the rate of return for the S&P 500 given it trailed the rate of return for the NASDAQ.
d. determine the probability the rate of return for the DJIA exceeded the rate of return for the S&P 500 given it exceeded the rate of return for the NASDAQ.