416 CHAPTER 8 Hypothesis Testing 29. Large Sample and a Small Difference It has been said that with really large samples, even very small differences between the sample mean and the claimed population mean can appear to be significant, but in reality they are not significant. Test this statement using the claim that the mean IQ score of adults is 100, given the following sample data: n = 1,000,000, x = 100.05, s = 15. Based on this sample, is the difference between x = 100.05 and the claimed mean of 100 statistically significant? Does that difference have practical significance? 30.Interpreting Power For the sample data in Exercise 23 “Cell Phone Radiation,” the hypothesis test has power of 0.9127 of supporting the claim that m 6 1.6W>kg when the actual population mean is 1.0 W>kg. Interpret this value of the power, then identify the value of b and interpret that value. (For the t test in this section, a “noncentrality parameter” makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.) 31. Finding Critical t Values When finding critical values, we often need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by calculating t = 3df # 1eA2>df - 12 where df = n - 1, e = 2.718, A = z18# df + 32>18# df + 12, and z is the critical z score. Use this approximation to find the critical t score for Exercise 28 “Army Height,” using a significance level of 0.05. Compare the results to the critical t score of 1.645 found from technology. Does this approximation appear to work reasonably well? 32.Hypothesis Test with Known S a. How do the results from Example 1 in this section change if s is known to be 1.99240984 g? Does the knowledge of s have much of an effect on the results of this hypothesis test? b. In general, can knowledge of s have much of an effect on the results of a hypothesis test of a claim about a population mean m? 8-3 Beyond the Basics Testing Claims About s or s2 Objective Conduct a hypothesis test of a claim made about a population standard deviation s or population variance s 2. Notation n = sample size s = sample standard deviation s2 = sample variance s = population standard deviation s 2 = population variance KEY ELEMENTS Key Concept An important goal of business and industry is to improve quality of goods and>or services by reducing variation. A hypothesis test can be used to confirm that an improvement has occurred by confirming that a relevant standard deviation has been lowered. This section presents methods for conducting a formal hypothesis test of a claim made about a population standard deviation s or population variance s 2. The methods of this section use the chi-square distribution that was first introduced in Section 7-3. The assumptions, test statistic, P-value, and critical values are summarized as follows. 8-4 Testing a Claim About a Standard Deviation or Variance
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