Researchers conducted a randomized, double-blind study to measure the effects of the drug olanzapine on patients diagnosed with bipolar disorder. A total of 115 patients with a DSM-IV diagnosis of bipolar disorder were randomly divided into two groups. Group 1 (n_{1} = 55) received 5 to 20 mg per day of olanzapine, while group 2 (n_{2} = 60) received a placebo. The effectiveness of the drug was measured using the Young–Mania rating scale total score with the net improvement in the score recorded. The results are presented in the table. Does the evidence suggest that the experimental group experienced a larger mean improvement than the control group at the α = 0.01 level of significance?
Group 1 | Group 2 | |
sample size | 55 | 60 |
sample mean | 14.8 | 8.1 |
sample st. dev. | 12.5 | 12.7 |
Let μ_{1} denote the mean rating score improvement with
olanzapine
and μ_{2} the mean rating score improvement with a
placebo.
Conditions:
a) The necessary conditions for Welch's t-test____
(are / are not) satisfied for
this data.
Rejection Region:
b) We are performing a -tailed _____(left /
right / two) test.
c) The critical value(s) for this test is/are ____. (Report any values as they appear in the table. If there are two critical values, report them both, separated only by a single space. Remember to sketch the rejection region.)
Test Statistic:
d) The test statistic for this test is t0 = _____. (Round to 3
decimal places, if applicable.)
Conclusion:
e) We _____(reject / fail to reject) H0.
f) The data ___ (does / does not) provide significant evidence that
the mean rating score improvement for patients taking olanzapine is
larger than the mean improvement for patients taking a placebo.
g) The P-value for this test is _____. (Report this value exactly as it appears in Minitab Express).
Solution
a) The necessary conditions for Welch's t-test are not satisfied for this data.
Rejection Region: the rejection region for this two-tailed test is R={F:F<0.496 or F>1.996}.
b) We are performing a -tailed left test.
c) The critical value(s) for this test is −2.36
d) The test statistic for this test is t0 = 2.847
e) We fail to reject H0.
f) The data does not provide significant evidence that the mean rating score improvement for patients taking olanzapine is larger than the mean improvement for patients taking a placebo.
g) The P-value for this test is 0.9974
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