In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss studying the relationship between on-the-job accidents and smoking. Cooper and Emory describe the study as follows:

Suppose a manager implementing a smoke-free workplace policy is interested in whether smoking affects worker accidents. Since the company has complete reports of on-the-job accidents, she draws a sample of names of workers who were involved in accidents during the last year. A similar sample from among workers who had no reported accidents in the last year is drawn. She interviews members of both groups to determine if they are smokers or not.

The sample results are given in the following table.

(a) For each row and column total in the above table, find the corresponding row/column percentage. (Round your answers to 2 decimal places.)

(b) For each cell in the above table, find the corresponding cell, row, and column percentages. (Round your answers to 2 decimal places.)

(c) Use the MINITAB output in the above to test the hypothesis that the incidence of on-the-job accidents is independent of smoking habits. Set α = .01.

(Click to select)Do not rejectReject H₀.

(d) Is there a difference in on-the-job accident occurrences between smokers and nonsmokers?

Conclude there is (Click to select)no differencedifference between smokers and nonsmokers.

Refer to the gasoline sales time series data in the given table.

The following frequency table summarizes a set of data. What is the five-number summary?

Select the correct answer below:

A company that produces computers claims that that the average life of one of their computers is 8 years. A sample of 12 computers shows a sample mean life of 7.8 years, with a population standard deviation of 0.2 years. Does the data suggest that the average life of one of the computers is not 8 years at 0.05 level significance? Assume computer lifetimes are normally distributed.

1. Give null and alternate hypothesis

2. Give test statistic and P value, state conclusion

3. State what type 1 and type 2 errors would be

A sample of 30 commuters in the area of a certain city yielded the accompanying commute times, in minutes. Preliminary data analyses indicate that the t-interval procedure can reasonably be applied. Find and interpret a 95% confidence interval for the mean commute time of all commuters in the area of the city (note: xbar = 28.20 minutes and s = 9.39 minutes)

Comparison/Contrast Outline

Attending a Historically Black College or University versus attending another type of institution of higher learning.

In its 2018 State of the First Amendment survey, the Freedom Forum Institute found that 40 percent of respondents could not recall any of the freedoms protected by the First Amendment. You decide to build a distribution for how many respondents could not recall any of the First Amendments. You take a random sample of 10 Americans. 1. What are the assumptions of a binomial distribution? Does this example match those assumptions? 2. What is the probability that the sample has exactly n successes, for n=1,2,3…10? 3. Plot the probabilities that were calculated in problem 2. 4. Find the probability that the sample has at least 5 successes. 5. Find the probability that the sample has at most 3 successes.

Many people believe that unusual behavior is more likely to occur during a full moon. As a test for empirical evidence to support this belief, suppose that you categorized the visits of new clients to a community health unit over a one-year period by lunar phases and found the following distribution of visits: Full moon 62, new moon 50, first quarter 60, and third quarter 56.

Answer the following questions:

1. What are the null and alternate hypotheses?

2. What are the expected values for each of the categories?

3. What is the chi-square obtained?

4. What is the critical value?

5. What is your statistical decision? Justify your answer.

6. What is your conclusion?

A t statistic was used to conduct a test of the null hypothesis H₀: µ = 11 against the alternative H_a: µ ≠ 11, with a p-value equal to 0.042. A two-sided confidence interval for µ is to be considered. Of the following, which is the largest level of confidence for which the confidence interval will NOT contain 11?

A 90% confidence level

A 92% confidence level

A 96% confidence level

A 97% confidence level

A 98% confidence level

2) A company makes the housing for a mechanical component used in lawn mowers. The critical dimension, ?, of the housing is Beta distributed with the following parameters: ? = 12.7 inches; ? = 13.5 inches; ? = 5 and ? = 7. To be acceptable, however, the dimension should be between 12.8 and 13.3 inches.

Determine:

(a) The mean and standard deviation of the dimension.

(b) The probability that a randomly selected housing will be acceptable. (Hint: You can use Microsoft Excel or a similar software for the calculation step)

(c) The company mentioned assumes that the critical dimension is normally distributed with the mean and standard deviation matching the original distribution. What is the probability that a randomly selected housing will be acceptable under this different assumption? Comment on the discrepancy from the previous answer.

In the Journal of Marketing Research (November 1996), Gupta studied the extent to which the purchase behavior of scanner panels is representative of overall brand preferences. A scanner panel is a sample of households whose purchase data are recorded when a magnetic identification card is presented at a store checkout. The table below gives peanut butter purchase data collected by the A. C. Nielson Company using a panel of 2,500 households in Sioux Falls, South Dakota. The data were collected over 102 weeks. The table also gives the market shares obtained by recording all peanut butter purchases at the same stores during the same period.

(a) Show that it is appropriate to carry out a chi-square test.

Each expected value is ≥               

(b) Test to determine whether the purchase behavior of the panel of 2,500 households is consistent with the purchase behavior of the population of all peanut butter purchasers. Assume here that purchase decisions by panel members are reasonably independent, and set α = .05. (Round your answers χ²to 2 decimal places and χ².05 to 3 decimal places.)

2. A researcher for Netflix wants to know if people have different preferences for two shows: Friends and The Office.  The researcher recruits 7 people.  Each person watches five minutes of Friends and rates the show on a scale of 0-10, where 0 means they hate it and 10 means they love it.  Then each person watches five minutes of The Office rates the show on a scale of 0-10.  Assume that you are working at the .05 level of significance. The researcher obtains the following data:

1. State the appropriate null and alternative hypotheses (in symbols, referring to the population means).       

2. Identify the critical value(s).

3. Calculate  .

4. Calculate the t statistic.  (The appropriate standard error that you need in the denominator when you compute t is 0.87.)

5. State your decision about the null hypothesis.

6. State the conclusion in terms of the alternative hypothesis (research question).

7. Compute Cohen’s d as an estimate of the effect size.

Let X1 and X2 be independent UNIF(0,1) random variables and consider the transformations Y1= X1X2 and Y2 =X1/X2. Find the joint pdf of Y1 and Y2 and indicate their joint support of Y1 and Y2. Show Work.

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is not 30g. The mean weight for a random sample of 16b ball bearings is 28.4g with a standard deviation of 4.5g. At the 0.05 significance level, test the claim that the sample comes from a population with a mean not equal to 30g. Find the critical value(s) and critical region. Identify the null and alternative hypotheses, test statistic, critical value(s) and critical region, as indicated, and state the final conclusion that addresses the problem. Show all seven steps.

Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):

Use the above data to develop and estimated regression equation and interpret the coefficients. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3400. Finally, test the significance of the slope coefficient.