Question

7.97 Suppose you want to test H?: ? = 500 against H?: ? > 500 using ? = .05. The population in question is normally distributed with standard deviation 100. A random sample of size n = 25 will be used. a. Sketch the sampling distribution of x? assuming that H? is true. b. Find the value of x??, that value of x? above which the null hypothesis will be rejected. Indicate the rejection region on your graph of part a. Shade the area above the rejection region and label it ?. c. On your graph of part a, sketch the sampling distribution of x? if ? = 550. Shade the area under this distribution that corresponds to the probability that x? falls in the nonrejection region when ? = 550. Label this area ?. d. Find ?. e. Compute the power of this test for detecting the alternative H?: ? = 550. 7.98 Refer to Exercise 7.97. a. If ? = 575 instead of 550, what is the probability that the hypothesis test will incorrectly fail to reject H?? That is, what is ?? b. If ? = 575, what is the probability that the test will correctly reject the null hypothesis? That is, what is the power of the test? c. Compare ? and the power of the test when ? = 575 to the values you obtained in Exercise 7.97 for ? = 550. Explain the differences.

          7.97 Suppose you want to test H?: ? = 500 against H?: ? > 500 using ? = .05. The population in question is normally distributed with standard deviation 100. A random sample of size n = 25 will be used.
a. Sketch the sampling distribution of x? assuming that H? is true.
b. Find the value of x??, that value of x? above which the null hypothesis will be rejected. Indicate the rejection region on your graph of part a. Shade the area above the rejection region and label it ?.
c. On your graph of part a, sketch the sampling distribution of x? if ? = 550. Shade the area under this distribution that corresponds to the probability that x? falls in the nonrejection region when ? = 550. Label this area ?.
d. Find ?.
e. Compute the power of this test for detecting the alternative H?: ? = 550.
7.98 Refer to Exercise 7.97.
a. If ? = 575 instead of 550, what is the probability that the hypothesis test will incorrectly fail to reject H?? That is, what is ??
b. If ? = 575, what is the probability that the test will correctly reject the null hypothesis? That is, what is the power of the test?
c. Compare ? and the power of the test when ? = 575 to the values you obtained in Exercise 7.97 for ? = 550. Explain the differences.

7.97 Suppose you want to test H?: ? = 500 against H?: ? > 500 using ? = .05. The population in question is normally distributed with standard deviation 100. A random sample of size n = 25 will be used.
a. Sketch the sampling distribution of x? assuming that H? is true.
b. Find the value of x??, that value of x? above which the null hypothesis will be rejected. Indicate the rejection region on your graph of part a. Shade the area above the rejection region and label it ?.
c. On your graph of part a, sketch the sampling distribution of x? if ? = 550. Shade the area under this distribution that corresponds to the probability that x? falls in the nonrejection region when ? = 550. Label this area ?.
d. Find ?.
e. Compute the power of this test for detecting the alternative H?: ? = 550.
7.98 Refer to Exercise 7.97.
a. If ? = 575 instead of 550, what is the probability that the hypothesis test will incorrectly fail to reject H?? That is, what is ??
b. If ? = 575, what is the probability that the test will correctly reject the null hypothesis? That is, what is the power of the test?
c. Compare ? and the power of the test when ? = 575 to the values you obtained in Exercise 7.97 for ? = 550. Explain the differences.

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