An RCT was designed to test the effectiveness of naltrexone, an opiate receptor antagonist, as a treatment for alcohol dependence. Subjects with chronic severe alcohol dependence were randomly assigned to either 3 months of naltrexone treatment or 3 months of placebo treatment. The number of drinks per drinking day was compared between the two groups. Let μ1= population mean number of drinks per drinking day for those on Naltrexone and μ2= population mean number of drinks per drinking day for those on placebo. The data from the study are summarized in the table below. Naltrexone (n1 = 196) Placebo (n2=195) Mean Number of drinks per drinking day Xbar1=10.5 Xbar2=9.3 Standard Deviation of Number of drinks per drinking day S1 = 80 S2 = 7.0 The investigators want to test whether there is a significant difference between the two groups using a 5% significance level. 1. What is the most appropriate test to address the investigators’ research question? a. Pearson’s Chi-Squared Test b. ANOVA c. Two-sample t-test assuming unequal variances d. Paired t-test e. Two-sample t-test assuming equal variances 2. Write the correct null and alternative hypothesis for the appropriate test 3. Using one of the probability tables provided to you, compute the p-value corresponding to the test statistic value from part (c) as accurately as possible. Which range does the p-value fall in? What is your conclusion for the hypothesis test based on this p-value? a. 0.005 < p < 0.01 b. 0.01 < p < 0.02 c. 0.10 < p < 0.20 d. 0.02 < p < 0.05 e. 0.05 < p < 0.10

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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An RCT was designed to test the effectiveness of naltrexone, an opiate receptor antagonist, as a treatment for alcohol dependence. Subjects with chronic severe alcohol dependence were randomly assigned to either 3 months of naltrexone treatment or 3 months of placebo treatment. The number of drinks per drinking day was compared between the two groups. Let μ1= population mean number of drinks per drinking day for those on Naltrexone and μ2= population mean number of drinks per drinking day for those on placebo. The data from the study are summarized in the table below.

Naltrexone
(n1 = 196)

Placebo

(n2=195)

Mean Number of drinks per
drinking day

Xbar1=10.5

Xbar2=9.3

Standard Deviation of Number
of drinks per drinking day

S1
= 80

S2
= 7.0

The investigators want to test whether there is a significant difference between the two groups using a 5% significance level.

1. What is the most appropriate test to address the investigators’ research question?

a. Pearson’s Chi-Squared Test

b. ANOVA

c. Two-sample t-test assuming unequal variances

d. Paired t-test

e. Two-sample t-test assuming equal variances

2. Write the correct null and alternative hypothesis for the appropriate test

3. Using one of the probability tables provided to you, compute the p-value corresponding to the test statistic value from part (c) as accurately as possible. Which range does the p-value fall in? What is your conclusion for the hypothesis test based on this p-value?

a. 0.005 < p < 0.01

b. 0.01 < p < 0.02

c. 0.10 < p < 0.20

d. 0.02 < p < 0.05

e. 0.05 < p < 0.10

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Follow-up Question

the the 95% confidence interval for the true difference in mean number of drinks per drinking day between those taking Naltrexone and those taking placebo would:

a. Include the estimated difference in the means.

b. Include 0 and the estimated difference in the means.

c. Include 0.

d. Not include 0.

e. Not include 0 and include the estimated difference in the means.

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Follow-up Question

The 95% confidence interval for the true difference in mean number of drinks per drinking day between those taking Naltrexone and those taking placebo would:

Include the estimated difference in the means.

Include 0 and the estimated difference in the means.

Include 0.

Not include 0.

Not include 0 and include the estimated difference in the means.

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