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It is desired to test H0: = 75 against Ha: < 75 using =
Chapter 7, Problem 99E(choose chapter or problem)
It is desired to test \(H_0: \mu=75\) against \(H_{\mathrm{a}}: \mu<75\) using \(\alpha=.10\). The population in question is uniformly distributed with standard deviation 15 . A random sample of size 49 will be drawn from the population.
a. Describe the (approximate) sampling distribution of \(\bar{x}\) under the assumption that \(H_0\) is true.
b. Describe the (approximate) sampling distribution of \(\bar{x}\) under the assumption that the population mean is 70 .
c. If \(\mu\) were really equal to 70 , what is the probability that the hypothesis test would lead the investigator to commit a Type II error?
d. What is the power of this test for detecting the alternative \(H_{\mathrm{a}}: \mu=70\)?
Questions & Answers
QUESTION:
It is desired to test \(H_0: \mu=75\) against \(H_{\mathrm{a}}: \mu<75\) using \(\alpha=.10\). The population in question is uniformly distributed with standard deviation 15 . A random sample of size 49 will be drawn from the population.
a. Describe the (approximate) sampling distribution of \(\bar{x}\) under the assumption that \(H_0\) is true.
b. Describe the (approximate) sampling distribution of \(\bar{x}\) under the assumption that the population mean is 70 .
c. If \(\mu\) were really equal to 70 , what is the probability that the hypothesis test would lead the investigator to commit a Type II error?
d. What is the power of this test for detecting the alternative \(H_{\mathrm{a}}: \mu=70\)?
ANSWER:Step 1 of 5
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