A new pain reliever, namely Pain Reliever A, has just been invented. To study how soon it can bring relief to patients, data has been collected from a random sample of 256 patients. The mean time to relief for the sample is 18.5 minutes and the standard deviation for the sample is 10 minutes. (a) What is the 95% confidence interval for the average relief time of Pain Reliever A? (b) To determine whether it is worthwhile to launch Pain Reliever A, you need to compare its effectiveness with Pain Reliever B, the pain reliever that is currently used in hospitals. Pain Reliever B is known to relieve pains in a mean time of 20 minutes. Would you conclude that Pain Reliever A is more effective than Pain Reliever B in reducing the mean time till relief? (c) With a sample mean of 18.5 and a sample standard deviation of 10 minutes, how large does a sample need to be in order for you to conclude with 99.7% confidence that Pain Reliever A is more effective than Pain Reliever B?
A new pain reliever, namely Pain Reliever A, has just been invented. To
study how soon it can bring relief to patients, data has been collected from a random
sample of 256 patients. The mean time to relief for the sample is 18.5 minutes and the
standard deviation for the sample is 10 minutes.
(a) What is the 95% confidence interval for the average relief time of Pain
Reliever A?
(b) To determine whether it is worthwhile to launch Pain Reliever A, you
need to compare its effectiveness with Pain Reliever B, the pain reliever that is
currently used in hospitals. Pain Reliever B is known to relieve pains in a mean
time of 20 minutes. Would you conclude that Pain Reliever A is more effective
than Pain Reliever B in reducing the mean time till relief?
(c) With a sample mean of 18.5 and a sample standard deviation of 10
minutes, how large does a sample need to be in order for you to conclude with
99.7% confidence that Pain Reliever A is more effective than Pain Reliever B?
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