# Basic+Business+Statistics%2c+9th+edition - CHAPTER 10 10.7...

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Unformatted text preview: CHAPTER 10 10.7 (a) H : μ 1 = μ 2 Light bulbs produced by machine 1 have the same mean life expectancy as light bulbs produced by machine 2. H 1 : μ 1 ≠ μ 2 Light bulbs produced by machine 1 have a different mean life expectancy as light bulbs produced by machine 2. Decision rule: If Z < – 1.96 or Z > 1.96, reject H . Test statistic: Z = ( X 1 – X 2 ) – ( μ 1 – μ 2 ) σ 1 2 n 1 + σ 2 2 n 2 = (375 – 362) – 0 110 2 25 + 125 2 25 = 0.39 Decision: Since Z calc = 0.39 is between the critical bounds of ± 1.96, do not reject H . There is not enough evidence to conclude that light bulbs produced by machine 1 have a different mean life expectancy than light bulbs produced by machine 2. (b) p- value = 2(1.0 – 0.6517) = 0.6966 The probability of obtaining samples whose means differ by (375 – 362) = 13 hours or more when the null hypothesis is true is 0.6966. 10.9 Assuming that the variance of the weight loss of the low-fat diet and low-carb diet are the same, the appropriate test to perform is the pooled-variance t test. (a) H : μ 1 = μ 2 H 1 : μ 1 ≠ μ 2 (b) A Type I error is committed when one concludes that there is a difference in mean weight loss between the two diets when there is not significant difference. (c) A Type II error is committed when one concludes that there is not significant difference in mean weight loss between the two diets when there is indeed significant difference. (d) PHStat output: Data Hypothesized Difference Level of Significance 0.05 Population 1 Sample Sample Size 100 Sample Mean 7.6 Sample Standard Deviation 3.2 Population 2 Sample Sample Size 100 Sample Mean 6.7 Sample Standard Deviation 3.9 Intermediate Calculations Population 1 Sample Degrees of Freedom 99 Population 2 Sample Degrees of Freedom 99 Total Degrees of Freedom 198 Pooled Variance 12.725 Difference in Sample Means 0.9 t-Test Statistic 1.784015 Two-Tailed Test Lower Critical Value-1.97202 138 Chapter 10: Two-Sample Tests Upper Critical Value 1.972016 p-Value 0.075953 Do not reject the null hypothesis Test statistic: 1 2 1 2 2 2 1 2 1 2 ( – ) – ( – ) X X t S S n n μ μ = + = 1.7840 Decision: Since t calc = 1.7840 is between the critical bounds of ± 1.97, do not reject H . There is no evidence of a difference in the mean weight loss of obsess patients between the low-fat and low-carb diets. 10.13 (a) H : 1 2 μ μ = where Populations: 1 = Line A, 2 = Line B H 1 : 1 2 μ μ ≠ Decision rule: d.f. = 25. If | t| > 2.0595, reject H . Test statistic: 1 2 1 2 5 2 1 2 ( ) ( ) (8.005 7.997) 0 1 1 1 1 7.26 10 11 16 p X X t S n n μ μ------ = = × + + =2.3972 Since t = 2.3972 > 2.0595 or p-value = 0.0243 < 0.05, reject H . There is sufficient evidence of a difference in the mean weight of cans filled on the two lines....
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