# Statistic Multiple Choice Questions

The following information is referenced in questions 15 through 19.

The Framingham Heart Study was a landmark study in epidemiology in that it was the first prospective study of cardiovascular disease and identified the concept of risk factors and their joint effects. The study began in 1948 and 4,434 randomly selected residents of Framingham initially enrolled in the study. Participants were between 32 and 70 years old at enrollment. At the time of enrollment, 56% of the participants were female, 49% of the participants were smokers at the time of enrollment, and 26% percent had clinically diagnosed cardiovascular disease. You are a researcher who has recently become privy to this historical data. Of particular interest is whether sex was associated with the risk of cardiovascular disease (CVD) in the cohort participants and the population from which they were sampled. CVD was coded 1 if the participant had cardiovascular disease at the time of enrollment, and 0 if the participant did not have cardiovascular disease at the time of enrollment. The following logistic regression results, all which relate the log odds of having CVD to various predictor sets, are based on this baseline data on 4,434 subjects:

Model Predictors Regression Coefficient Standard Error

A Sex -0.85 0.07

B Smoking, Sex -0.85 0.07

C Age, Sex -0.92 0.07

D Smoking, Age, Sex -0.87 0.07

1 : sex is an indicator variable coded as 1 for female, 0 for male

2: smoking is an indicator variable coded as 1 for smoker, 0 for non-smoker

3: age is continous, measured in years

15. Which of the following statements best describes the unadjusted relationship between sex and cardiovascular disease (CVD)?

a. Female subjects in the sample had a lower risk of having CVD than males in the sample, but this association is not statistically significant . (p > .05)

b. Female subjects in the sample had a lower risk of having CVD than males in the sample, and this association is statistically significant . (p < .05)

c. Female subjects in the sample had a higher risk of having CVD than males in the sample, but this association is not statistically significant . (p > .05)

d. Female subjects in the sample had a higher risk of having CVD than males in the sample, and this association is statistically significant . (p < .05)

16. Using the above reported logistic regression results, estimate a 95% confidence interval for the adjusted odds ratio of cardiovascular disease for females compared to males, adjusted for age and smoking status.

a. 0.36 to 0.48

b. 2.08 to 2.75

c. -1.01 to -0.73

d. 0.73 to 1.01

17. After seeing these results, a colleague claims that the relationship between cardiovascular disease (CVD) and sex in this sample is not confounded by participants age and/or smoking status. The best justification for this argument given the above information is:

a.The estimated odds ratio of cardiovascular disease for females compared to males is substantially different for smokers and non-smokers.

b.The estimate crude odds ratio and sex-adjusted odds ratios of cardiovascular disease for smokers compared to non-smokers are similar.

c.The estimated odds ratios of cardiovascular disease for females compared to males are similar across all four regression models presented (A,B, C,D)

d.The estimated odds ratios of cardiovascular disease for females compared to males are substantially different across at least some of the four regression models presented (A,B, C,D)

e.None of the above justifications make sense, because odds ratios can not be estimated from the given regression results.

18.Suppse you were interested in using the results of any of the 4 logistic regression models to estimate the risk of CVD (the proportion of patients who have CVD) using patients characteristics included in the model. Would this be allowable?

a.Yes, because the study design allows for risk to be estimated

b.No, because you can only estimate odds ratios using logistic regression.

c.No, because this is a case-control study and you can not estimate risk from a case-control study design.

19. Another colleague wants to investigate whether smoking status modifies the relationship between the risk of cardiovascular disease and sex. (ie: your colleague is interested in a statistical interaction between sex and smoking)Which of the following actions would need to be taken to answer your colleague's question?

a. No further analyses would be needed, as the logistic regression results presented above contain enough information to investigate this potential interaction.

b. You would need to perform another logistic regression that allows for separate estimates of the CVD/sex relationship for smokers and non- smokers.

c. Nothing could be done to investigate interaction, because interaction can not be investigated using logistic regression.

See attached file for full problem description.

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#### Solution Preview

Please see the attached file.

The following information is referenced in questions 15 through 19.

The Framingham Heart Study was a landmark study in epidemiology in that it was the first prospective study of cardiovascular disease and identified the concept of risk factors and their joint effects. The study began in 1948 and 4,434 randomly selected residents of Framingham initially enrolled in the study. Participants were between 32 and 70 years old at enrollment. At the time of enrollment, 56% of the participants were female, 49% of the participants were smokers at the time of enrollment, and 26% percent had clinically diagnosed cardiovascular disease. You are a researcher who has recently become privy to this historical data. Of particular interest is whether sex was associated with the risk of cardiovascular disease (CVD) in the cohort participants and the population from which they were sampled. CVD was coded 1 if the participant had cardiovascular disease at the time of enrollment, and 0 if the participant did not have cardiovascular disease at the time of enrollment. The following logistic regression results, all which relate the log odds of having CVD to various predictor sets, are based on this baseline data on 4,434 subjects:

Model Predictors Regression Coefficient Standard Error

A Sex -0.85 0.07

B Smoking, Sex -0.85 0.07

C Age, Sex -0.92 0.07

D Smoking, Age, Sex -0.87 0.07

1 : sex is an indicator variable coded as 1 for female, 0 for ...

#### Solution Summary

This problem set includes five multiple choice questions involving logistic regression, odds ratios, and the interpretation of data/statistical tests.

Statistics multiple choice questions

Use the following information to answer questions 11-16:

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?

Product FIFO (F) LIFO (L)

1 225 221

2 119 100

3 100 113

4 212 200

5 248 245

11. What is the null hypothesis if we are to create a right tailed test ?

A)

B)

C)

D)

12. What is the alternate hypothesis?

A)

B)

C)

D)

13. What are the degrees of freedom?

A) 4

B) 5

C) 15

D) 10

E) 9

14. If you use the 5% level of significance, what is the critical t value?

A) +2.132

B) - 2.776

C) + 2.262

D) - 2.228

15. What is the value of calculated t?

A) +0.93

B) - 2.776

C) +2.47

D) -2.028

16. What is the decision at the 5% level of significance?

A) Fail to reject the null hypothesis and conclude LIFO is more effective.

B) Reject the null hypothesis and conclude LIFO is more effective.

C) Reject the alternate hypothesis and conclude LIFO is more effective.

D) Fail to reject the null hypothesis and conclude LIFO is not more effective.