A40 TRY IT YOURSELF ANSWERS Chapter 6 Section 6.1 1. 2.85 2. 0.43 hour 3. (2.42, 3.28) 4. (19.49, 20.36); (19.38, 20.47); (19.30, 20.55); As the confidence level increases, so does the width of the interval. 5. (22.4, 23.4) [Tech: (22.5, 23.4)]; Because of the larger sample size, the confidence interval is slightly narrower. 6. 40; Because of the larger margin of error, the sample size needed is smaller. Section 6.2 1. 1.721 2. (157.6, 166.4); (154.6, 169.4) 3. (9.08, 10.42); (8.94, 10.56); The 90% confidence interval is slightly narrower. 4. Use a t-distribution because s is not known and the population is normally distributed. Section 6.3 1. 14% 2. (0.12, 0.16) 3. (0.475, 0.565) 4. (1) 1692 (2) 1591 Section 6.4 1. 42.557, 17.708 2. Population variance: (0.98, 2.36), (0.91, 2.60) Standard deviation: (0.99, 1.54), (0.96, 1.61) Chapter 7 Section 7.1 1. (1) The mean is not 74 months. m ≠ 74 H0: m = 74; Ha: m ≠ 74 (claim) (2) The variance is less than or equal to 2.7. s 2 … 2.7 H0: s 2 … 2.7 (claim); Ha: s 2 7 2.7 (3) The proportion is more than 24%. p 7 0.24 H0: p … 0.24; Ha: p 7 0.24 (claim) 2. A type I error will occur when the actual proportion is less than or equal to 0.01, but you reject H0. A type II error will occur when the actual proportion is greater than 0.01, but you fail to reject H0. A type II error is more serious because you would be misleading the consumer, possibly causing serious injury or death. 3. (1) H0: The mean life of a certain type of automobile battery is 74 months. Ha: The mean life of a certain type of automobile battery is not 74 months. H0: m = 74; Ha: m ≠ 74 Two-tailed −z z P-value area z 1 2 P-value area 1 2 (2) H0: The variance of the life of a manufacturer’s home theater systems is less than or equal to 2.7. Ha: The variance of the life of a manufacturer’s home theater systems is greater than 2.7. H0: s 2 … 2.7; Ha: s 2 7 2.7 Right-tailed z z P-value area (3) H0: The proportion of homeowners who feel their house is too small for their family is less than or equal to 24%. Ha: The proportion of homeowners who feel their house is too small for their family is greater than 24%. H0: p … 0.24; Ha: p 7 0.24 Right-tailed z z P-value area 4. (1) There is enough evidence to support the claim that the mean life of a certain type of automobile battery is not 74 months. There is not enough evidence to support the claim that the mean life of a certain type of automobile battery is not 74 months. (2) There is enough evidence to support the realtor’s claim that the proportion of homeowners who feel their house is too small for their family is more than 24%. There is not enough evidence to support the realtor’s claim that the proportion of homeowners who feel their house is too small for their family is more than 24%. 5. (1) H0: m Ú 650; Ha: m 6 650 (claim) If you reject H0, then you will support the claim that the mean repair cost per automobile is less than $650. (2) H0: m = 98.6 (claim); Ha: m ≠ 98.6 If you reject H0, then you will reject the claim that the mean temperature is about 98.6°F. Section 7.2 1. (1) Fail to reject H0. (2) Reject H0. 2. 0.0436; Reject H0 because 0.0436 6 0.05. 3. 0.1010; Fail to reject H0 because 0.1010 7 0.01. 4. There is enough evidence at the 5% level of significance to support the claim that the average speed is greater than 35 miles per hour.
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