Question

An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly found in older patients. Thirteen patients are given the new drug and 13 patients are given the old drug. To avoid bias in the experiment, they are not told which drug is given to them. To check how the effectiveness depends on the age of patients, the following data have been collected.

To examine the differences between salaries of male and female middle managers of a large bank, 90 individuals were randomly selected, and two models were created with the following variables considered: Salary = the monthly salary (excluding fringe benefits and bonuses), Educ = the number of years of education, Exper = the number of months of experience, Train = the number of weeks of training, Gender = the gender of an individual; 1 for males, and 0 for females. Excel partial outputs corresponding to these models are available and shown below. Model A: Salary = β0 + β1Educ + β2Exper + β3Train + β4Gender + ε df SS MS F Regression 4 28,045,960.12 7,011,490.03 43.23 Residual 85 13,787,729.88 162,208.59 Total 89 41,833,690.00 Coefficients Standard Error t-stat p-value Intercept 4,663.31 365.37 12.76 1.85E-21 Educ 140.66 20.15 6.98 6.07E-10 Exper 3.36 0.47 7.17 2.54E-10 Train 1.17 3.72 0.31 0.7543 Gender 615.15 97.33 0.32 1.16E-08 Model B: Salary = β0 + β1Educ + β2Exper + β3Gender + ε df SS MS F Regression 3 28,029,969.88 9,343,323.29 58.21 Residual 86 13,803,720.12 162,508.37 Total 89 41,833,690.00 Coefficients Standard Error t-stat p-value Intercept 4,713.26 327.1967 14.40 1.21E-24 Educ 139.54 19.7253 7.07 3.78E-10 Exper 3.35 0.4649 7.20 2.10E-10 Gender 609.25 94.9920 6.41 7.39E-09 Assuming the same years of education and months of experience, what is the null hypothesis for testing whether the mean salary of males is greater than the mean salary of females using Model B? Multiple Choice H0: β3> 0 H0: β3 ≤ 0 H0: β3 ≥ 0 H0: β3 = 0

Old Drug:	Patient Age	21	28	33	33	38	43	48	53	53	58	63	67	52
	Effectiveness	56	55	61	54	58	65	64	61	69	71	66	70	60

The variables are
Effectiveness = the response variable measured on a scale from 0 to 100,
Age = the age of a patient (in years),
Drug = a dummy variable that is 1 for the new drug and 0 for the old drug.
The regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug, is estimated and the following results are obtained.

	Coefficients	Standard Error	t-stat	p-value
Intercept	47.04	3.1479	14.9423	5.31E-13
Age	0.34	0.0665	5.0610	4.55E-05
Drug	−40.86	4.0798	−10.016	1.17E-09
Age × Drug	0.70	0.0879	7.9385	6.71E-08

Which of the following is the estimated regression model for the new drug?

Multiple Choice

• EffectivenessˆEffectiveness^ = 47.04 + 0.34Age – 40.86Drug + 0.70Age × Drug

• EffectivenessˆEffectiveness^ = 47.04 + 0.34Age

• EffectivenessˆEffectiveness^  = 47.04 + 0.34Age + 0.70Age × Drug

• EffectivenessˆEffectiveness^  = 6.18 + 1.04Age

Answer 1

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