In a pilot study, a company's new cholesterol-reducing drug outperforms the currently available drug. If the data provide convincing evidence that the mean cholesterol reduction with the new drug is more than 10 milligrams per deciliter of blood (mg/dl) greater than with the current drug, the company will begin the expensive process of mass-producing the new drug. For the 14 subjects who were assigned at random to the current drug, the mean cholesterol reduction was 54.1 mg/dl with a standard deviation of 11.93 mg/dl. For the 15 subjects who were randomly assigned to the new drug, the mean cholesterol reduction was 68.7 mg/dl with a standard deviation of 13.3 mg/dl. Graphs of the data reveal no outliers or strong skewness.) Based on your conclusion in part (a), could you have made a Type I error or a Type II error? Justify your answer.

Question

Mathematics

Harley Aguilar

16 September, 00:22

In a pilot study, a company's new cholesterol-reducing drug outperforms the currently available drug. If the data provide convincing evidence that the mean cholesterol reduction with the new drug is more than 10 milligrams per deciliter of blood (mg/dl) greater than with the current drug, the company will begin the expensive process of mass-producing the new drug. For the 14 subjects who were assigned at random to the current drug, the mean cholesterol reduction was 54.1 mg/dl with a standard deviation of 11.93 mg/dl. For the 15 subjects who were randomly assigned to the new drug, the mean cholesterol reduction was 68.7 mg/dl with a standard deviation of 13.3 mg/dl. Graphs of the data reveal no outliers or strong skewness.) Based on your conclusion in part (a), could you have made a Type I error or a Type II error? Justify your answer.

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Yurem Braun · Answer 1

Type I error: rejecting a true null hypothesis.

Step-by-step explanation:

A Type I error happens when a true null hypothesis is rejected.

A Type II error happens when a false null hypothesis is failed to be rejected.

In this case, the claim that was tested was if the drug was effective. This claim is expressed in the alternative hypothesis and, in this case, the conclusion is that there was evidence to reject the null hypothesis.

Then, if the null hypothesis was rejected, the only type of error that could have been comitted is a Type I error: rejecting a true null hypothesis.