Suppose you are testing two treatments for an illness, Treatment A and Treatment B. Assume that your populations for Treatments A and B are both normal, and both have variances o?. Treatment A is a new treatment, and Treatment B is the established treatment, The effects of the two treatments are measured on a numerical scale. You want to show that Treatment A is better than Treatment B. Through long experience, you know that the average result of Treatment B gives a numerical score of 70. Moreover you also know that the standard deviation is approximately 2. You make the null hypothesis that µA = 80. (a) Suppose you have 1,000 volunteers for Treatment A and 900 for Treatment B. You take a random sample of size n = TA = 120. What, if anything, can you conclude? 100, and you find that for Treatment A you have (b) What are the probabilities for Type I and Type II errors under the assumption H, : MA 80?

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Suppose you are testing two treatments for an illness, Treatment A and Treatment B. Assume
that your populations for Treatments A and B are both normal, and both have variances o?.
Treatment A is a new treatment, and Treatment B is the established treatment, The effects
of the two treatments are measured on a numerical scale. You want to show that Treatment
A is better than Treatment B. Through long experience, you know that the average result
of Treatment B gives a numerical score of 70. Moreover you also know that the standard
deviation is approximately 2. You make the null hypothesis that uA = 80.
(a) Suppose you have 1,000 volunteers for Treatment A and 900 for Treatment B. You
take a random sample of size n
100, and you find that for Treatment A you have
TA
120. What, if anything, can you conclude?
(b) What are the probabilities for Type I and Type II errors under the assumption Ho :
HA = 80?
Transcribed Image Text:Suppose you are testing two treatments for an illness, Treatment A and Treatment B. Assume that your populations for Treatments A and B are both normal, and both have variances o?. Treatment A is a new treatment, and Treatment B is the established treatment, The effects of the two treatments are measured on a numerical scale. You want to show that Treatment A is better than Treatment B. Through long experience, you know that the average result of Treatment B gives a numerical score of 70. Moreover you also know that the standard deviation is approximately 2. You make the null hypothesis that uA = 80. (a) Suppose you have 1,000 volunteers for Treatment A and 900 for Treatment B. You take a random sample of size n 100, and you find that for Treatment A you have TA 120. What, if anything, can you conclude? (b) What are the probabilities for Type I and Type II errors under the assumption Ho : HA = 80?
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