A study in the Journal of the American Medical Association

A study in the Journal of the American Medical Association (February 20, 2008) found that patients who go into cardiac arrest while in the hospital are more likely to die if it happens after 11 pm. The study investigated 58,593 cardiac arrests during the day or evening. Of those, 11,604 survived to leave the hospital. There were 28,155 cardiac arrests during the shift that began at 11 pm, commonly referred to as the graveyard shift. Of those, 4,139 survived for discharge. The following contingency table summarizes the results of the study:

a. Specify the competing hypotheses to determine whether a patient’s survival depends on the time at which he/she experiences cardiac arrest.

b. Calculate the value of the test statistic and the p-value.

c. At the 1% significance level, is the timing of when a cardiac arrest occurs dependent on whether or not the patient survives for discharge? Given your answer, what type of recommendations might you give to hospitals?

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According to a report by the Centers for Disease Control

According to a report by the Centers for Disease Control and Prevention (CDC), 36.5% of American adults are obese (Adult Obesity Facts, August 29, 2017). Among ethnic groups in general, African American women are more overweight than Caucasian women, but African American men are less obese than Caucasian men. Sarah Weber, a recent college graduate, is curious to determine if the same pattern also exists in her hometown on the West Coast. She randomly selects 220 African American adults and 300 Caucasian adults for the analysis. The following table contains the sample information.

a. Test if the proportion of obese African American men is less than the proportion of obese Caucasian men at α = 0.05.

b. Test if the proportion of obese African American women is more than the proportion of obese Caucasian women at α = 0.05.

c. Test if the proportion of obese African American adults differs from the proportion of obese Caucasian adults at the 5% significance level.

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The Marketing Manager at Foodco, a large grocery store, wants

The Marketing Manager at Foodco, a large grocery store, wants to determine if store display location influences sales of a particular grocery item. He instructs employees to rotate the display location of that item every week and then tallies the weekly sales at each location over a 24-week period (8 weeks per location). The following sales (in $) were obtained. Assume that sales are normally distributed.

a. Specify the competing hypotheses to test whether there are some differences in the mean weekly sales across the three store display locations.

b. At the 5% significance level, what is the conclusion to the test?

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Although founded only in 2004, Facebook has nearly 2 billion

Although founded only in 2004, Facebook has nearly 2 billion active users, of which 50% log on to Facebook on any given day. In a survey by Facebook, young users were asked about their
preference for delivering the news about breaking up a relationship (The Wall Street Journal, November 27–28, 2010). One of the shocking results was that only 47% of users preferred to
break the news in person. A researcher decides to verify the survey results of Facebook by taking her own sample of 200 young Facebook users. The preference percentages from Facebook
and the researcher’s survey are presented in the following table.

At the 5% level of significance, test if the researcher’s results are inconsistent with the survey results conducted by Facebook. Provide the details.

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Important risk factors for high blood pressure reported by the

Important risk factors for high blood pressure reported by the National Institute of Health include weight and ethnicity. High blood pressure is common in adults who are overweight and are African-American. According to the American Heart Association, the systolic pressure (top number) should be below 120. In a recent study, a public policy researcher in Atlanta surveyed 150 adult men in the 55-60 age group. Data was collected on their systolic pressure, weight (in pounds), and race (Black = 1 for African-American; 0 otherwise); a portion of the data is shown in the following table.

a. Estimate and interpret the effect of Weight and Black on Systolic. Predict the systolic pressure of black and non-black adult men with a weight of 180 pounds.

b. Extend the model in part a to include the interaction between Weight and Black. Predict the systolic pressure of black and non-black adult men with a weight of 180 pounds.

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A sociologist is looking at the relationship between consumption expenditures

A sociologist is looking at the relationship between consumption expenditures of families in the United States (Consumption in $), family income (Income in $), and whether or not the family lives in an urban or rural community (Urban = 1 if urban, 0 otherwise). She collects data on 50 families across the United States, a portion of which is shown in the accompanying table.

a. Estimate: Consumption = β0 + β1 Income + ε. Compute the predicted consumption expenditures of a family with income of $75,000.

b. Include a dummy variable Urban to predict consumption for a family with income of $75,000 in urban and rural communities.

c. Include a dummy variable Urban and an interaction variable (Income × Urban) to predict consumption for a family with income of $75,000 in urban and rural communities.

d. Which of the preceding models is most suitable for the data? Explain.

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A sociologist is studying the relationship between consumption expenditures of

A sociologist is studying the relationship between consumption expenditures of families in the United States (Consumption in $), family income (Income in $), and whether or not the family lives in an urban or rural community (Urban = 1 if urban, 0 otherwise). She collects data on 50 families, a portion of which is shown in the accompanying
table.

a. Estimate Consumption = β0 + βIncome + β2 Urban + ε. Use the estimated model to predict the consumption expenditure of urban families with an income of $80,000. What is the corresponding consumption expenditure of rural families?

b. Estimate Consumption = β0 + β1 Income + β2 Rural + ε where the dummy variable Rural equals 1 if rural, 0 otherwise. Use the estimated model to predict the consumption expenditure of urban families with an income of $80,000. What is the corresponding consumption expenditure of rural families?

c. Interpret the results of the two models.

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One of the theories regarding initial public offering (IPO) pricing

One of the theories regarding initial public offering (IPO) pricing is that the initial return y (the percentage change from offer to open price) on an IPO depends on the price revision x (the percentage change from pre-offer to offer price). Another factor that may influence the initial return is a high-tech dummy variable that equals 1 for high-tech firms and 0 otherwise. The following table shows a portion of the data on 264 IPO firms from January 2001 through September 2004.

a. Estimate y = β0 + β1x + β2d + ε where the dummy variable d equals 1 for firms that are high-tech. Use the estimated model to predict the initial return of a high-tech firm with a 10% price revision. Find the corresponding predicted return of a firm that is not high-tech.

b. Estimate y = β0 + β1x + β2d + ε where the dummy variable d equals 1 for firms that are not high-tech. Use the estimated model to predict the initial return of a high-tech firm with a 10% price revision. Find the corresponding predicted return of a firm that is not high-tech.

c. In the above two models, determine if the dummy variable is significant at the 5% level.

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