A study was performed to test the effectiveness of a new treatment for migraines. There were 125 patients in the study. Of these, 60 were randomly assigned to receive the standard treatment and 65 to receive the new treatment. All were instructed to take the medication at the onset of their next migraine and to notice if the pain of their migraine felt reduced after half an hour. Fifty patients receiving the new treatment reported reduced pain, compared with only 40 of the patients receiving the standard treatment. The results seem to favor the new treatment, but could the difference just be due to chance? In this problem, consider the null hypothesis that the percentage of patients with a reduction in pain is the same between the two treatments, versus the alternative hypothesis that the percentages are different. (a) Under the null hypothesis, the difference in the sample percentages is expected to be ___%. The standard error for the difference is estimated to be ___%. (b) Calculate the two-sample z test statistic. (c) Calculate the p-value. (d) Do you reject the null hypothesis? (e) State your conclusion in the context of the original problem.
A study was performed to test the effectiveness of a new treatment for migraines. There were 125 patients in the study. Of these, 60 were randomly assigned to receive the standard treatment and 65 to receive the new treatment. All were instructed to take the medication at the onset of their next migraine and to notice if the pain of their migraine felt reduced after half an hour. Fifty patients receiving the new treatment reported reduced pain, compared with only 40 of the patients receiving the standard treatment. The results seem to favor the new treatment, but could the difference just be due to chance?
In this problem, consider the null hypothesis that the percentage of patients with a reduction in pain is the same between the two treatments, versus the alternative hypothesis that the percentages are different.
(a) Under the null hypothesis, the difference in the sample percentages is expected to be ___%. The standard error for the difference is estimated to be ___%.
(b) Calculate the two-sample z test statistic.
(c) Calculate the p-value.
(d) Do you reject the null hypothesis?
(e) State your conclusion in the context of the original problem.
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