Review Exercises 575 20. A quality technician claims that the variance of the insert diameters produced by a plastic company’s new injection mold for automobile dashboard inserts is less than the variance of the insert diameters produced by the company’s current mold. The table shows samples of insert diameters (in centimeters) for both the current and new molds. At a = 0.05, can you support the technician’s claim? New 9.611 9.618 9.594 9.580 9.611 9.597 Current 9.571 9.642 9.650 9.651 9.596 9.636 New 9.638 9.568 9.605 9.603 9.647 9.590 Current 9.570 9.537 9.641 9.625 9.626 9.579 Section 10.4 In Exercises 21 and 22, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. 21. The table shows the monthly electric bills (in dollars) for a sample of households from four regions of the United States. At a = 0.10, can you conclude that the mean monthly electric bill is different in at least one of the regions? (Adapted from U.S. Energy Information Administration) Northeast Midwest South West 150.71 92.37 119.16 83.07 100.53 100.23 97.62 95.43 125.89 108.15 131.84 106.83 120.04 95.52 127.92 80.04 121.62 113.26 144.73 75.63 97.18 99.02 150.45 101.92 105.07 117.82 109.46 127.29 115.47 120.60 134.07 168.21 103.60 120.74 113.93 95.83 22. The table shows the annual incomes (in dollars) for a sample of families from four regions of the United States. At a = 0.05, can you conclude that the mean annual income of families is different in at least one of the regions? (Adapted from U.S. Census Bureau) Northeast Midwest South West 78,123 63,930 62,623 79,496 71,388 73,543 64,182 77,904 81,251 71,602 59,668 74,113 74,379 65,357 59,373 72,191 75,210 62,907 61,536 75,668 70,119 63,073 76,415 66,833
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