HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION in .NET

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9-4 HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION
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(b) What is the P-value of the test statistic computed in part (a) (c) Compute the power of the test if the true mean dissolved oxygen concentration is as low as 3. (d) What sample size would be required to detect a true mean dissolved oxygen concentration as low as 2.5 if we wanted the power of the test to be at least 0.9 9-39. Consider the cigar tar content data rst presented in Exercise 8-82. (a) Can you support a claim that mean tar content exceeds 1.5 Use 0.05 (b) What is the P-value of the test statistic computed in part (a) (c) Compute the power of the test if the true mean tar content is 1.6. (d) What sample size would be required to detect a true mean tar content of 1.6 if we wanted the power of the test to be at least 0.8 9-40. Exercise 6-22 gave data on the heights of female engineering students at ASU. (a) Can you support a claim that mean height of female engineering students at ASU is 65 inches Use 0.05 (b) What is the P-value of the test statistic computed in part (a) (c) Compute the power of the test if the true mean height is 62 inches.
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(d) What sample size would be required to detect a true mean height of 64 inches if we wanted the power of the test to be at least 0.8 9-41. Exercise 6-24 presented data on the concentration of suspended solids in lake water. (a) Test the hypotheses H0: 55 versus H1: 55, use 0.05. (b) What is the P-value of the test statistic computed in part (a) (c) Compute the power of the test if the true mean concentration is as low as 50. (d) What sample size would be required to detect a true mean concentration as low as 50 if we wanted the power of the test to be at least 0.9 9-42. Exercise 6-25 describes testing golf balls for an overall distance standard. (a) Can you support a claim that mean distance achieved by this particular golf ball exceeds 280 yards Use 0.05. (b) What is the P-value of the test statistic computed in part (a) (c) Compute the power of the test if the true mean distance is 290 yards. (e) What sample size would be required to detect a true mean distance of 290 yards if we wanted the power of the test to be at least 0.8
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9-4 HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION
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Sometimes hypothesis tests on the population variance or standard deviation are needed. When the population is modeled by a normal distribution, the tests and intervals described in this section are applicable.
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9-4.1
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The Hypothesis Testing Procedures
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Suppose that we wish to test the hypothesis that the variance of a normal population 2 equals a speci ed value, say 2, or equivalently, that the standard deviation is equal to 0. Let X1, 0 X2, p , Xn be a random sample of n observations from this population. To test H0: H1: we will use the test statistic: 1n
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(9-26)
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(9-27)
2 2 If the null hypothesis H0: 2 0 is true, the test statistic X 0 de ned in Equation 9-27 follows the chi-square distribution with n 1 degrees of freedom. This is the reference
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CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE
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/2
/2
2 1 /2, n 1 2 /2, n 1
0 (b)
2 2 0
2 , n 1
2 1 , n 1
x (c)
2 2 0,
Figure 9-10 (b) H1: 2
Reference distribution for the test of H0: 2 2 2 0 , and (c) H1: 0.
with critical region values for (a) H1:
2 distribution for this test procedure. Therefore, we calculate 2 , the value of the test statistic X 0 , 0 2 2 and the null hypothesis H0: 0 would be rejected if 2 0 2 2, n 1