Although arsenic is known to be a poison, it also has some beneficial medicinal uses. In one study of the use of arsenic to treat acute promyelocytic leukemia (APL), a rare type if blood cancer, APL patients were given an arsenic compound as part of their treatment. Of those receiving arsenic, 32% were in remission and showed no signs of leukemia in subsequent examination. It is known that 18% of APL patients go into remission after conventional treatment. Suppose that the study had included 100 randomly selected patients. Is there sufficient evidence to conclude that the proportion in remission for the arsenic treatment is greater than 0.18, the remission proportion for conventional treatment? a. Test the hypothesis at the 0.01 significance level. b. Construct and interpret a 99% confidence interval for the true proportion of APL patients who go into remission after using arsenic. Does the inference drawn from this interval match the conclusion from the test that you did in part (a)? c. Suppose that we are interested in hypothesis testing and confidence intervals for a single proportion. In your own words, explain why it possible for the conclusion of a hypothesis test done at significance level 0.05 to be different from the inference drawn from a 95% confidence interval that is constructed from the same data used to conduct the test.
Although arsenic is known to be a poison, it also has some beneficial medicinal uses. In one study of the use of arsenic to treat acute promyelocytic leukemia (APL), a rare type if blood cancer, APL patients were given an arsenic compound as part of their treatment. Of those receiving arsenic, 32% were in remission and showed no signs of leukemia in subsequent examination. It is known that 18% of APL patients go into remission after conventional treatment. Suppose that the study had included 100 randomly selected patients. Is there sufficient evidence to conclude that the proportion in remission for the arsenic treatment is greater than 0.18, the remission proportion for conventional treatment?
a. Test the hypothesis at the 0.01 significance level.
b. Construct and interpret a 99% confidence interval for the true proportion of APL patients who go into remission after using arsenic. Does the inference drawn from this interval match the conclusion from the test that you did in part (a)?
c. Suppose that we are interested in hypothesis testing and confidence intervals for a single proportion. In your own words, explain why it possible for the conclusion of a hypothesis test done at significance level 0.05 to be different from the inference drawn from a 95% confidence interval that is constructed from the same data used to conduct the test.
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