Consider the experiment of tossing two dice. Your random variable is D, the square of difference of the numbers showing on the faces of the two dice.

Show its probability distribution in the form of a table.

Find the mean, median and mode of the distribution.

Find the variance of D.

What type of skewness does the probability distribution represent?

Is the Chebychev inequality satisfied for c=1 and c=2? Show the calculations.

According to Harper's Index, 50% of all federal inmates are serving time for drug dealing. A random sample of 15 federal inmates is selected.

(a) What is the probability that 10 or more are serving time for drug dealing? (Round your answer to three decimal places.)


(b) What is the probability that 6 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)


(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)

Each value represents the number of mistakes (defects) found on a student loan application. Values for 50 consecutive loan applications are given. Calculate the appropriate centerline and 3-sigma control limits for the c-chart, and then plot the data and create a control chart. Does the process appear to be in a state of statistical control? Why or why not?

Upper control limit (UCL) =

Centerline (CL) =

Lower control limit (LCL) =

Process in statistical control?

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.10, he will reject the shipment. He will test the hypotheses H 0 : p = 0.10 , H a : p < 0.10 . He selects an SRS of 100 potatoes from the over 2000 potatoes on the truck. Suppose that 6 of the potatoes sampled are found to have major defects. Which of the following is true? Strictly speaking, the inspector should take a larger sample in order to more safely apply the large sample significance test for proportion. The inspector might reach the wrong conclusion about the lot of potatoes, whether he returns the shipment or not. The inspector will decide to reject the shipment because there's weak evidence that the proportion of potatoes with serious defects is less than 0.10. All of the above statements are true.

Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for a sample of 8 men was 34 minutes per day. The standard deviation was 19 minutes per day. The mean listening time for a sample of 10 women was also 34 minutes, but the standard deviation of the sample was 7 minutes. Use a two-tailed test and at 0.02 significance level, can we conclude that there is a difference in the variation in the listening times for men and women? (Round your answer to 3 decimal places.) The test statistic is . Decision: H0:σ21=σ22.

Assume that 80% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:

a. There are some lefties (≥ 1) among the 5 people.

b. There are exactly 3 lefties in the group.

c. There are at least 4 lefties in the group.

d. There are no more than 2 lefties in the group

. e. How many lefties do you expect?

f. With what standard deviation?

1. Major television networks have never seemed to have issues showing commercials for beer and other alcoholic beverages. Even though adult viewers tend to enjoy the commercials, most adults seem to think that the commercials target teenagers and young adults (those under 21 years old). To study this belief, the networks conducted a joint poll of viewers and asked them if they felt that beer and other alcoholic beverage commercials targeted teenagers and young adults. The results of the survey are as follows

a. Are the sample sizes large enough such that inferences about the differences between two population proportion can be made? If so, calculate a 99% confidence interval for the difference in the proportions of those older than 30 and those 30 or younger that believe alcoholic beverage commercials targeted teenagers and young adults. Interpret the interval.

b. Based on the data, can the networks conclude that the percentage of viewers who believe beer and alcoholic beverage commercials target teenagers and young adults is significantly higher in the over 30 age group than in the 30 or younger age group? Construct the 10 steps of hypothesis testing using α = 0.01 to answer the question.

Step 1 (Define the hypotheses to be tested in plain English)

Step 2 (Select the appropriate statistical measure, such as the population mean, proportion, or
              variance.)

Step 3 (Determine whether the alternative hypothesis should be one-sided or two-sided.)

Step 4 (State the hypotheses using the statistical measure found in Step 2)

Step 5 (Specify α, the level of the test.)

Step 6 (Select the appropriate test statistic based on the information at hand and the
              assumptions you willing to make.)

Step 7 (Determine the critical value of the test statistic.)

Step 8 (Collect sample data and compute the value of the test statistic.)

Step 9 (Make the decision.)

Step 10 (State the conclusion in terms of the original question.)

For a study, 375 patients were randomly assigned tor eceive a daily dose of levvofloxacin, and 363 were given placebo. In the group receiving treatment, fever was present in 243 patients for the duration of neutroenia, whereas feverw as experienced by 308 patients in the placebo group. Using this information, determine whether or not the proportion of patients with fever differed between the two groups at the 1% level of significance. State the null and alternative hypothesis, manually calculate the test statistic and determine its p-value. Then state your decision and conclusion.

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99 % confidence assuming s equals 13.9 based on earlier​ studies? Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size​ required? A​ 99% confidence level requires nothing subjects. ​(Round up to the nearest​ subject.) A 90 % confidence level requires nothing subjects. ​(Round up to the nearest​ subject.)

99 % confidence is

90 confidence is

How does the decrease in confidence affect the sample size​ required?

A. Decreasing the confidence level increases the sample size needed.

B. Decreasing the confidence level decreases the sample size needed.

C. The sample size is the same for all levels of confidence.

Consider a binomial experiment with 16 trials and probability 0.60 of success on a single trial.

(a) Use the binomial distribution to find the probability of exactly 10 successes.

(b) Use the normal distribution to approximate the probability of exactly 10 successes.

(c) Compare the results of parts (a) and (b).

Group 1: 4.2, 4.2, 3.4

Group 2: 4.5, 2.1, 2.3

Group 3: 1.2, 0.3, -0.3, 2.3

Use the Bonferronni method to test each of the 3 possible hypotheses at the 3% significance level.

(a) Find the value of the test statistic for each of the 3 possible hypotheses.

(b) Which pairs of means are significantly different (using the Bonferronni method at the 3% significance level?

M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown.

Confidence Interval for Small n

Choose the color of M&M’s you will be working with for this project

Color:

Using the collected data below from a single fun-sized bag, provide the frequency and proportion of M&M’s in your color of choice.

Number of M&M's in your color:

Total number of M&M's:

            Proportion of M&M's in your color:

Construct a 95% confidence interval for the proportion of M&M’s one can expect to find in the color of your choice.

Check the requirements for constructing a confidence interval for the proportion are satisfied. Show your work.

The conditions might not be satisfied, depending on how many candies were in your bag. If the conditions are not met, what could you do?

Part 2: Confidence Interval for Larger n

Now, use the data collected below from a collection of fun-sized bags to provide the frequency and proportion of M&M’s in your original color of choice.

Number of M&M's in your color:

Total number of M&M's:

Proportion of M&M's in your color:

Construct a 95% confidence interval for the proportion of M&M’s one can expect to find in the color of your choice.

Write an interpretation of your confidence interval specific to your color.

Check the requirements for constructing a confidence interval for the proportion are satisfied. Show your work. (See the note in the blue box on page 426)

How are confidence intervals affected by sample size?

How does the margin of error for the confidence interval in Part 1 compare to the margin of error for your confidence interval in Part 2? (compute both and compare)

Does the confidence interval you constructed in Part 2 contain the claimed proportion given by Mars Inc?

Do you believe the claims given by Mars Inc?

The following is a payoff table giving profits for various situations.

States of Nature Alternatives A B C D

Alternative 1 120 140 170 160

Alternative 2 210 130 140 120

Alternative 3 120 140 110 190

Do Nothing 0 0 0 0

a. What decision would a pessimist make?

b. What decision would an optimist make?

c. What decision would be made based on the realism criterion, where the coefficient of realism is 0.60?

d. What decision would be made based on the equally likely criterion?

e. What decision would be made based on the minimax regret criterion? Suppose now that the probabilities of the 4 states of nature are known, that is, the probability to observe A is 30%, the probability to observe B is 35%, the probability to observe C is 20%, and the probability to observe D is 15%. Answer the following

f. What decision would be made based on the expected monetary value?

g. What is the EVPI