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Analyzing Journal Article Results Researchers (Brian G. Feagan et al. “Erythropoietin with Iron Supplementation to Prevent Allogeneic Blood Transfusion in Total Hip Joint Arthroplasty,” Annals of Internal Medicine, Vol. 133, No. 11) wanted to determine whether epoetin alfa was effective in increasing the hemoglobin concentration in patients undergoing hip arthroplasty. A complete medical history and physical of the patients was performed for screening purposes and eligible patients were identified. The researchers used a computer-generated schedule to assign the patients to the high-dose epoetin group, low-dose epoetin group, or placebo group. The study was double-blind. Based on ANOVA, it was determined that there were significant differences in the increase in hemoglobin concentration in the three groups with a -value less than 0.001. The mean increase in hemoglobin in the high-dose epoetin group was 19.5 grams per liter (g/L), the mean increase in hemoglobin in the low-dose epoetin group was 17.2 g/L, and mean increase in hemoglobin in the placebo group was 1.2 g/L.

(a) Why do you think it was necessary to screen patients for eligibility?

(b) Why was a computer-generated schedule used to assign patients to the various treatment groups?

(c) What does it mean for a study to be double-blind? Why do you think the researchers desired a double-blind study?

(d) Interpret the reported P-value.

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Case Study

Feeling Lucky? Well, Are You?

In fiscal year (FY) 2013–2014 (July 2013–June 2014), the Florida Lottery generated $5.37 billion in total sales. Over that period, the state spent $37.5 million on advertising to promote its various games. Rand Advertising is interested in gaining access to this lucrative market. You are assigned the task of preparing a report on the lottery sales structure for three of Florida’s online (nonscratch-off ticket) games: Fantasy 5, Lucky Money, and Lotto. Your findings will become part of a proposal by Rand to the Florida Lottery.
In Fantasy 5, a player picks five numbers from 1 to 36, at $1 per play. Drawings are held seven days a week. If there is no jackpot winner for a drawing, the money allocated for the top prize rolls down to the next prize tier (4 of 5).
The Lucky Money game costs $1 per ticket. Players pick four numbers from 1 to 47 and one Lucky Money number from 1 to 22. Drawings are held on Tuesdays and Fridays. If there is no jackpot winner for a drawing, the money allocated for the top prize rolls over to the next drawing, adding to the total of the next jackpot. The prize structures for both games is as shown.

In Lotto, players pick six numbers from 1 to 53, at $1 per play. Drawings are held on Wednesdays and Saturdays. If there is no jackpot winner, the top prize is rolled over to the next drawing. It is difficult to win the Lotto jackpot, so there are numerous jackpot rollovers. Rollovers make it difficult to determine an estimated prize payout per winner. However, the odds structure is shown in the table at the top of the next column.

To conduct your study, you have obtained the sales figures for each of the three games by district sales office for one week. These data are as follows:

Are the numbers of tickets sold for each lottery game and sales district independent? Construct a bar graph that represents the conditional distribution of game by sales district. Does this graphical evidence support your conclusion regarding the relationship between the type of game and the sales district? Explain.
Additionally, you are interested in the daily sales structure for the various districts. The following are the numbers of tickets sold each day for a randomly selected week for the three games in District 1.

Does the evidence suggest that the proportion of Fantasy 5 sales is the same for each day of the week? Perform a similar test for Lucky Money and Lotto.
Write a report detailing your assumptions, analyses, findings, and conclusions.

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In problem 12.10, you were asked to develop the equation of a regression model to predict the sales by the amount spent on mobile advertisements. Using this regression model and the data given in problem 12.10 (and provided here again), solve for the predicted values of  and the residuals. Comment on the size of the residuals.

Problem 12.10

The Swedish research institute Berg Insight estimated that mobile marketing and advertising sales would grow from 1.3 billion euros to 10 billion euros between 2009 and 2015. But is mobile advertising effective in increasing sales? Suppose the data below are pairs of the amount spent on mobile advertisements and the amount of sales for a nine-year period for an online retailer. Use these data to develop the equation of the regression model to predict the amount of sales by the amount spent on mobile advertisements. Discuss the meaning of the slope.

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Putting It Together: Psychological Profiles Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain (RAP) or recurring headaches. A total of 210 children and adolescents were studied and their psychological profiles were graded according to the Child Behavior Checklist 4–18 (CBCL). Children were stratified in two age groups: 4 to 11 years and 12 to 18 years. The results of the study are summarized in the following table:

(a) Compute the sample standard deviations for each group.

(b) What sampling method was used for each treatment group? Why?

(c) Use a two sample -test for independent samples to determine if there is a significant difference in mean CBCL scores between the control group and the RAP group (assume that both samples are simple random samples).

(d) Is it necessary to check the normality assumption to answer part (c)? Explain.

(e) Use the one-way ANOVA procedure with  to determine if the mean CBCL scores are different for the three treatment groups.

(f) Based on your results from parts (c) and (e), can you determine if there is a significant difference between the mean scores of the RAP group and the headache group? Explain.

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