For the below questions, refer to the following study and the SAS output below:A study was conducted on 60 patients to examine the analgesic effects of treatments on elderly patients with neuralgia. Two test treatments and a placebo were compared. The response variable is whether the patient reported pain or not. Researchers recorded the following variables:

PAIN: patient reported pain (1=yes, 0=no)

TX: treatment (2=test treatment A, 1=test treatment B, 0=placebo)

AGE: age of the patient when the treatment began (in years)

SEX: sex (1=male, 0=female)

DURATION: duration of complaint before the treatment began (in months)

Testing Global Null Hypothesis: BETA=0

TestChi-SquareDFPr > ChiSq

Likelihood Ratio32.76755<.0001

Score25.666650.0001

Wald14.451250.0130

Type 3 Analysis of Effects

Wald

EffectDFChi-SquarePr > ChiSq

tx212.53100.0019

age17.29770.0069

sex15.29460.0214

duration10.03150.8591

Analysis of Maximum Likelihood Estimates

StandardWald

ParameterDFEstimateErrorChi-SquarePr > ChiSq

Intercept1-17.40666.69146.76690.0093

tx11-3.70851.140710.57000.0011

tx21-3.18171.01619.80490.0017

age10.26210.09707.29770.0069

sex111.83220.79635.29460.0214

duration1-0.005860.03300.03150.8591

Odds Ratio Estimates

Point95% Wald

EffectEstimateConfidence Limits

tx1 vs 0A0.0030.229

tx2 vs 0B0.0060.304

ageC1.0751.572

sex1 vs 0D1.31229.750

durationE0.9321.061

1.Using a 0.05 significance level, what decision and conclusion should you make regarding the omnibus null hypothesis?

a.Becausep-value < 0.05, we reject H₀and conclude that all of the independent variables are significant factors associated with reporting pain.

b.Becausep-value < 0.05, we reject H₀and conclude that none of the independent variables are significant factors associated with reporting pain.

c.Because p-value < 0.05, we reject H₀and conclude that at least one of the independent variables is a significant factor associated with reporting pain.

d.Becausep-value < 0.05, we fail to reject H₀and conclude that all of the independent variables are significant factors associated with reporting pain.

e.Becausep-value < 0.05, we fail to reject H₀and conclude that none of the independent variables are significant factors associated with reporting pain.

2.Are there any reference cells in this problem? If so, what are they?

a.No, there are no reference cells.

b.Yes, reference cell is younger age.

c.Yes, reference cells are treatment A and male.

d.Yes, reference cells are placebo and female.

e.Both b and c

f.Both b and d

3.How many dummy variables need to be included in the model for TX?

a.3

b.2

c.1

d.0

e.Cannot be determined from the given information

4.What is the estimated odds ratio for reporting pain for a 65-year-old compared to a 60-year-old, controlling for all other variables in the model?

a.0.26

b.1.30

c.1.69

d.3.71

e.7.30

5.Given the estimated odds of reporting pain for a 65-year-old male in treatment group A with a complaint duration of 14 days is 0.165, what is the corresponding risk of reporting pain?

a.0.03

b.0.14

c.0.17

d.1.18

e.1.80