A clinical trial wished to compare the number of sleepless nights that patients
ID: 3133547 • Letter: A
Question
A clinical trial wished to compare the number of sleepless nights that patients endured in a sleep trial using Ambien. For each of the 10 patients enrolled to take Ambien, a control was matched to each case based on gender, race, and age. The following table shows each of the 10 pairs, with the number of sleepless nights experienced by the Ambien group versus the Placebo group (no Ambien used). Investigators wish to know if the the placebo group experiences significantly more sleepless nights than those taking Ambien? The standard deviation (Sd) is 0.48.
What is the null hypothesis?
What is the research hypothesis?
What is the appropriate test statistic?
Z-test
t-test
F-test (ANOVA)
Chi-Square Goodness of Fit
Chi-Square Test of Independence
What is the critical value for the test statistic? Just give the number, not the name of the test. E.g. for Z-test, upper-tail, just write:
What is the test statistic for this study? Just give the number, not the name of the test. E.g. for Z-test, upper-tail, just write:
Interpret your findings. Remember to include magnitude, direction, significance, outcome measure, and groups being compared for full credit.
Z-test
t-test
F-test (ANOVA)
Chi-Square Goodness of Fit
Chi-Square Test of Independence
What is the critical value for the test statistic? Just give the number, not the name of the test. E.g. for Z-test, upper-tail, just write:
What is the test statistic for this study? Just give the number, not the name of the test. E.g. for Z-test, upper-tail, just write:
Interpret your findings. Remember to include magnitude, direction, significance, outcome measure, and groups being compared for full credit.
Explanation / Answer
What is the null hypothesis?
Ho: ud = u(x(ambien) - x(placebo)) >= 0 [ANSWER]
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What is the research hypothesis?
This is the alternative hypothesis,
Ha: ud = u(x(ambien) - x(placebo)) < 0 [ANSWER]
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What is the appropriate test statistic?
As this is a paired t test because of the small sample size,
OPTION B: T TEST [ANSWER]
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We set alpha = 0.05.
As we can see, this is a left tailed test.
As df = n - 1 = 9
Then the critical value of t is
tcrit = - 1.833112933 [ANSWER]
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Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 0.48
Calculating the mean of the differences (third column):
XD = -4.3
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = -8.958333333 [ANSWER, TEST STATISTIC]
***********************
As |t| > 1.833, we reject Ho at 0.05 level.
Hence, there is significant evidence that the true mean number of sleepless nights with Ambien is less than the Placebo group at 0.05 level. The best estimate for the mean difference of sleepless nights to be round 4.3 nights less for Ambien users.
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