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In: Statistics and Probability

In an experiment to test the effectiveness of a new sleeping aid, a sample of 12...

In an experiment to test the effectiveness of a new sleeping aid, a sample of 12 patients took the new drug, and a sample of 15 patients took a commonly used drug. Of the patients taking the new drug, the average time to fall asleep was 28.6 minutes with a sample standard deviation of 5.2 minutes, and for the patients taking the commonly used drug the average time was 30.7 minutes with a sample standard deviation of 4.1 minutes. Can you conclude that the mean time to sleep is less for the new drug? Assume that population standard deviations are the same. Take ? = 0.01.

a. Use P-value method to test the hypothesis.  

b. Find 99% confidence interval and use it to test the hypothesis.

c. Clearly write your conclusion.

d. If the true mean difference between the sleep times is 2 minutes, what is the probability that we can recognize it.

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Expert Solution

orchestra answered 1 year ago
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