preform a Monte Carlo simulation in R to generate the probability distribution of the sum of two die (for example 1st die is 2 and second die is 3 the random variable is 2+3=5). The R-script should print out (display in R-studio) or have saved files for the following well labeled results:

1. Histrogram or barchart of probability distribution

2. Mean of probability distribution

3. Standard deviation of probability distribution

Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently.

Let X = the minimum of the value from each die.
a. What is the probability mass function(pmf) of X?

b. Find the mean E[X] and variance V (X).

c. Write the cumulative distribution function (cdf) of X in a tabular form.

d. Write F(x) the cdf of X as a step function and give a rough sketch for this function.

For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is as follows. [You may find it useful to reference the t table.] ANOVA df SS MS F Significance F Regression 2 2,517.3 1,258.7 0.29 0.749 Residual 17 72,837.53 4,284.56 Total 19 75,354.8 Coefficients Standard Error t Stat p-value Intercept 716.6835 86.0322 8.330 0.000 Poverty 3.3717 4.7573 0.7090 0.488 Income 3.6612 14.3119 0.2560 0.801 b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related. H0: β1 ≤ 0; HA: β1 > 0 H0: β1 = 0; HA: β1 ≠ 0 H0: β1 ≥ 0; HA: β1 < 0 b-2. At the 5% significance level, what is the conclusion to the test? Do not reject H0 we cannot conclude that the poverty rate and the crime rate are linearly related. Reject H0 we can conclude that the poverty rate and the crime rate are linearly related. Do not reject H0 we can conclude that the poverty rate and the crime rate are linearly related. Reject H0 we cannot conclude that the poverty rate and the crime rate are linearly related. c-1. Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round "tα/2,df" value to 3 decimal places, and final answers to 2 decimal places.) c-2. Using the confidence interval, determine whether income influences the crime rate at the 5% significance level. Income is significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero. Income is not significant in explaining the crime rate, since its slope coefficient significantly differs from zero. Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero. Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero. d-1. Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate. H0: β1 = β2 = 0; HA: At least one β j > 0 H0: β1 = β2 = 0; HA: At least one β j < 0 H0: β1 = β2 = 0; HA: At least one β j ≠ 0 d-2. At the 5% significance level, are the poverty rate and income jointly significant in explaining the crime rate? No, since the null hypothesis is not rejected. Yes, since the null hypothesis is rejected. No, since the null hypothesis is rejected. Yes, since the null hypothesis is not rejected.

you are to create one 90%, one 95%, and one 99.7% confidence interval for the true proportion of online students

Raw data:

Survey Question: Do you have kids under the age of 18?

Yes - 15

No - 44

Total - 59

1. Summary of Data

2. A statement of what your variable X means

3. A statement of what your statistic means (with proper notation).

4. Your calculated statistic

5. The distribution for your variable (with proper notation)

6. Your check for normality

7. A statement of the what your population parameter means

8. Your work (Yup, show the steps out)

9. Your confidence interval

10. A conclusion

1. Confidence intervals for mean differences provide researchers with

2. Is the following statement true? Values between the LB and UB values of a 95% CI are all equally plausible values for a population parameter.

3. When computing a 95% CI for a population mean the ______ is used to compute the margin of error.

4. M = 28; SD = 4; N = 49; you need a 95% CI to estimate a population mean. What is the point estimate?

5. M = 28; SD = 4; N = 49; you need a 95% CI to estimate a population mean. What is the margin of error?

6. M = 28; SD = 4; N = 49; you need a 95% CI to estimate a population mean. What is the UB?

7. M = 28; SD = 4; N = 49; you need a 95% CI to estimate a population mean. What is the LB?

1. A researcher is interested to learn if the level of interaction a women in her 20s has with her mother influences her life satisfaction ratings. Below is a list of women who fit into each of four levels of interaction. Conduct a One-way ANOVA on the data to determine if there are differences between groups; does the level of interaction influence women’s ratings of life satisfaction? Report the results of the One-way ANOVA(copy and paste Chart). If significance is found, run the appropriate post-hoc test and report between what levels the significant differences were found. Report the test statistic using correct APA formatting and interpret the results.

In a city of 80,000 households, 800 were randomly sampled in a marketing survey by an auto manufacturer. To see how typical this city was, some statistics were collected: the average number of cars per household was 1.32, while the standard deviation for the number of cars per household was 0.8. Construct a 95% confidence interval for the average number of cars per household in the whole city.

For the following situations, develop the appropriate Ho and Ha and state what the consequences would be for Type 1 and Type 2 errors.

a. A company that manufactures one-half inch bolts selects a random sample of bolts to determine if the diameter of the bolts differs significantly from the required one-half inch.

b. A company that manufactures safety flares randomly selects 100 flares to determine if the flares last at least three hours on average.

c. a consumer group believes that a new sports coupe gets significantly fewer miles to the gallon than advertised on the sales sticker. To confirm this belief, they randomly select several of the new coupes and measure the miles per gallon.

1. Insomnia has become an epidemic in the United States. Much research has been done in the development of new pharmaceuticals to aide those who suffer from insomnia. Alternatives to the pharmaceuticals are being sought by sufferers. A new relaxation technique has been tested to see if it is effective in treating the disorder. Sixty insomnia sufferers between the ages of 18 to 40 with no underlying health conditions volunteered to participate in a clinical trial. They were randomly assigned to either receive the relaxation treatment or a proven pharmaceutical treatment. Thirty were assigned to each group. The amount of time it took each of them to fall asleep was measured and recorded. The data is shown below. Run an independent samples t-test to determine if the relaxation treatment is more effective than the pharmaceutical treatment at a level of significance of 0.05. copy and paste the chart from SPSS. Report the test statistic using correct APA formatting and interpret the results.

1) We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 270 had kids. Based on this, construct a 90% confidence interval for the proportion p of adult residents who are parents in this county. Provide the point estimate and margin of error. Give your answers as decimals, to three places.

P= __  ± __

2) You measure 36 textbooks' weights, and find they have a mean weight of 57 ounces. Assume the population standard deviation is 5.6 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places

__  < μ < __

3) You measure 49 dogs' weights, and find they have a mean weight of 53 ounces. Assume the population standard deviation is 9.2 ounces. Based on this, determine the point estimate and margin of error for a 90% confidence interval for the true population mean dog weight.
Give your answers as decimals, to two places.

μ= __ ± __ ounces

Use technology to construct the confidence intervals for the population variance sigmaσ squared2 and the population standard deviation sigmaσ. Assume the sample is taken from a normally distributed population.

c equals=0.99, ssquared2=12.96 n=27

The confidence interval for the population variance is

THIS IS NOT MEANT TO BE A SAMPLE TEST. EXAM QUESTIONS MAY NOT BE SIMILAR TO THOSE IN THIS REVIEW.

1. Read the values of the variable VOL in the dataset IQandBrainSize and find the proportion of sample values within 1, 2 and 3 sample standard deviations from the mean.

2. Nucryst Pharmaceutical, Inc. announced the results of its first human trial of NPI 32101, a topical form of its skin ointment. A total of 225 patients diagnosed with skin irritations were randomly divided into three groups as part of a double-blind, placebo-controlled study to test the effectiveness of the new topical cream. The first group received a 0.5% cream, the second group received a 1.0% cream, and the third group received a placebo. Groups were treated twice daily for a 6-week period.

1. Is this an observational study?

2. What are the treatments?

3. What does it mean for this study to be double-blind?

4. What is the control group for this study?

5. Identify the experimental units.

3. You have in R a data set dat consisting of persons’ names. Issue R commands to obtain a sample of size 100 from this population consisting of all the names other than “Aron”.

4. Consider a random sample of coins and record the year stamped on each. Would you expect the distribution of numbers to be symmetric or skewed? Why?

5.  A sample consists of seven points. Explain how to add one more item to the sample so that the median doesn’t change.

6. A uniform distribution takes values between 1 and 4. Draw the density. Show the scales on both axes.

7. Find the 90th percentile of a normal distribution with mean 23 and standard deviation 7.

8. You roll 4 dice. What is the probability of getting at least one 6?

9. These are the distributions of blood types in the US and Ireland. Choose one person in each country independently. What is the probability that they have the same blood type?

10. You toss two balanced coins independently. Let A be the event head on the first toss and let B be the event both tosses have the same outcome. Compute P(A), P(B), P(B|A). Are A, B independent?

11. A data set has Q1 = 54.5 and Q3 = 200. What values will be considered outliers?

12. When should relative frequencies be used when comparing two data sets? Why?

13. Describe the circumstances in which a bar graph is preferable to a pie chart. When is a pie chart preferred over a bar graph?

In a 1993 article in Accounting and Business Research, Meier, Alam, and Pearson studied auditor lobbying on several proposed U.S. accounting standards that affect banks and savings and loan associations. As part of this study, the authors investigated auditors’ positions regarding proposed changes in accounting standards that would increase client firms’ reported earnings. It was hypothesized that auditors would favor such proposed changes because their clients’ managers would receive higher compensation (salary, bonuses, and so on) when client earnings were reported to be higher. The following table summarizes auditor and client positions (in favor or opposed) regarding proposed changes in accounting standards that would increase client firms’ reported earnings. Here the auditor and client positions are cross-classified versus the size of the client firm.

You will need to type in the FOUR pieces of data into Minitab, along with column headings LARGE and SMALL (firms). Data go into the white cells in Minitab, starting with row 1. Column headings go in the grey shaded cells in Minitab. Do not type in the totals, as those are not new pieces of data.

a) Auditor Positions

Client Positions

(a) Test to determine whether auditor positions regarding earnings-increasing changes in accounting standards depend on the size of the client firm. Use α = .05. (Round your expected frequencies to 2 decimal places. Round your answer to 3 decimal places.)

x^2 =  ; so  (Click to select)  Reject  Do not reject   H₀: independence for auditor positions regarding earnings-increasing changes.

(b) Test to determine whether client positions regarding earnings-increasing changes in accounting standards depend on the size of the client firm. Use α = .05. (Round your answer to 3 decimal places.)

x^2 =  ; so  (Click to select)  Do not reject  Reject   H₀: independence for client positions regarding earnings-increasing changes.

(d) Does the relationship between position and the size of the client firm seem to be similar for both auditors and clients?

• Yes

• No

In a 1993 article in Accounting and Business Research, Meier, Alam, and Pearson studied auditor lobbying on several proposed U.S. accounting standards that affect banks and savings and loan associations. As part of this study, the authors investigated auditors’ positions regarding proposed changes in accounting standards that would increase client firms’ reported earnings. It was hypothesized that auditors would favor such proposed changes because their clients’ managers would receive higher compensation (salary, bonuses, and so on) when client earnings were reported to be higher. The following table summarizes auditor and client positions (in favor or opposed) regarding proposed changes in accounting standards that would increase client firms’ reported earnings. Here the auditor and client positions are cross-classified versus the size of the client firm.

You will need to type in the FOUR pieces of data into Minitab, along with column headings LARGE and SMALL (firms). Data go into the white cells in Minitab, starting with row 1. Column headings go in the grey shaded cells in Minitab. Do not type in the totals, as those are not new pieces of data.

a) Auditor Positions

(b) Client Positions

(a) Test to determine whether auditor positions regarding earnings-increasing changes in accounting standards depend on the size of the client firm. Use α = .05. (Round your expected frequencies to 2 decimal places. Round your answer to 3 decimal places.)

x2 =  ; so  (Click to select)  Do not reject  Reject   H₀: independence for auditor positions regarding earnings-increasing changes.

(b) Test to determine whether client positions regarding earnings-increasing changes in accounting standards depend on the size of the client firm. Use α = .05. (Round your answer to 3 decimal places.)

x2 =  ; so  (Click to select)  Do not reject  Reject   H₀: independence for client positions regarding earnings-increasing changes.

(d) Does the relationship between position and the size of the client firm seem to be similar for both auditors and clients?

• Yes

• No