For questions 47-53, refer to the following study and the accompanying SAS output: Tager et al. (1979, 1983) examined children’s pulmonary function in the absence or presence of smoking cigarettes. Their studies were some of the earliest attempts at systematic documentation regarding obvious signs of reduced pulmonary function from smoking and from exposure to second-hand smoke. Consider a cross-sectional subset from the Tager et. al. studies to examine the relationship between subjects’ forced expiratory volume (FEV) and their current smoking status while adjusting for age. FEV, which is the amount of air an individual can exhale in the first second of a forceful breath, is measured on a continuous scale (in liters). Smoking status is divided in two groups (1=smoker, 0=nonsmoker), and age is reported on a continuous scale (in years). The sample consists of 654 youths between the ages of 3 and 19 in East Boston during the middle to late 1970’s. Note that this is an observational study where the subjects self-select the smoking or nonsmoking groups. Using a 0.05 significance level and the given computer output, you need to test the claim that the mean FEV levels for smoking and nonsmoking youths differ significantly after controlling for age by answering the questions that follow.

These data were analyzed using two different models. Results from the analysis are provided below labeled SAS Output 1 and SAS Output 2. To answer some of the questions that follow, you need to fill in some critical pieces of information that have been deleted. 

47. What type of analysis should you perform to test the given hypothesis?

a. Linear regression

b. One-way ANOVA

c. Two-way ANOVA

d. ANCOVA

e. Logistic Regression 

48. In SAS Output 2, what number should you insert for the unexplained degrees of freedom?

a. 3

b. 4

c. 649 

d. 650

e. 653 

49. Which model is more appropriate for these data: the model in SAS Output 1 or the model in SAS Output 2? Which test statistic and p-value should you use to make this decision?

1. Output 1 because the interaction is not significant (F = 443.25, p-value < 0.0001).
2. Output 1 because the interaction is not significant (F = 317.11, p-value < 0.0001).
3. Output 1 because the interaction is not significant (F = 28.02, p-value < 0.0001).
4. Output 2 because the interaction is significant (F = 28.02, p-value < 0.0001).
5. Output 2 because the interaction is significant (F = 317.11, p-value < 0.0001).

50. In SAS Output 1, what is the value of the test statistic for the omnibus null hypothesis H0?

1. <0.0001
2. 6.70
3. 45.19
4. 443.25
5. 793.90

51. Do the smokers and nonsmokers differ significantly in their mean FEV levels? If so, how?

1. Yes, smokers have a significantly lower mean FEV level than nonsmokers.
2. Yes, smokers have a significantly higher mean FEV level than nonsmokers.
3. Yes, smokers have a significantly lower mean FEV level than nonsmokers at younger ages but higher mean FEV level at older ages.
4. Yes, smokers have a significantly higher mean FEV level than nonsmokers at younger ages but lower mean FEV level at older ages.
5. No, smokers and nonsmokers have the same mean FEV level. 

52. Consider the estimated model from SAS Output 2, which can be written as: