# Ch08 - Chapter 8 Interval Estimation Learning Objectives 1...

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8 - 1 Chapter 8 Interval Estimation Learning Objectives 1. Know how to construct and interpret an interval estimate of a population mean and / or a population proportion. 2. Understand and be able to compute the margin of error. 3. Learn about the t distribution and its use in constructing an interval estimate for a population mean. 4. Be able to determine the size of a simple random sample necessary to estimate a population mean and/or a population proportion with a specified level of precision. 5. Know the definition of the following terms: confidence interval margin of error confidence coefficient degrees of freedom confidence level

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Chapter 8 8 - 2 Solutions: 1. a. /5 / 4 0 . 7 9 x n σσ == = b. At 95%, zn σ /. ( / ) . 196 5 40 155 2. a. 32 ± 1.645 (/ ) 65 0 32 ± 1.4 or 30.6 to 33.4 b. 32 ± 1.96 ) 0 32 ± 1.66 or 30.34 to 33.66 c. 32 ± 2.576 ) 0 32 ± 2.19 or 29.81 to 34.19 3. a. 80 ± 1.96 (/ ) 15 60 80 ± 3.8 or 76.2 to 83.8 b. 80 ± 1.96 ) 15 120 80 ± 2.68 or 77.32 to 82.68 c. Larger sample provides a smaller margin of error. 4. Sample mean 160 152 156 2 x Margin of Error = 160 – 156 = 4 1.96( / ) 4 n = 1.96 / 4 1.96(15)/ 4 7.35 n = n = (7.35) 2 = 54 5. a. 1.96 / 1.96(5/ 49) 1.40 n b. 24.80 ± 1.40 or 23.40 to 26.20 6. .025 x ± 8.5 ± 1.96(3.5/ 300 ) 8.5 ± .4 or 8.1 to 8.9
Interval Estimation 8 - 3 7. .025 ( / ) 1.96(4000/ 60) 1012 zn σ == A larger sample size would be needed to reduce the margin of error. Section 8.3 can be used to show that the sample size would need to be increased to n = 246. 1.96(4000/ ) 500 n = Solving for n , shows n = 246 8. a. Since n is small, as assumption that the population is at least approximately normal is required. b. .025 ( / ) 1.96(5/ 10) 3.1 c. .005 (/ )2 . 5 7 6 ( 5 /1 0 )4 . 1 9. x ± .025 z (/ ) n 3.37 ± 1.96 (.28/ 120) 3.37 ± .05 or 3.32 to 3.42 10. a. xz n ± α /2 12,000 ± 1.645 (2200/ 245) 12,000 ± 231 or 11,769 to 12,231 b. 12,000 ± 1.96 12,000 ± 275 or 11,725 to 12,275 c. 12,000 ± 2.576 12,000 ± 362 or 11,638 to 12,362 d. Interval width must increase since we want to make a statement about µ with greater confidence. 11. a. .025 b. 1 - .10 = .90 c. .05 d. .01 e. 1 – 2(.025) = .95 f. 1 – 2(.05) = .90

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Chapter 8 8 - 4 12. a. 2.179 b. -1.676 c. 2.457 d. Use .05 column, -1.708 and 1.708 e. Use .025 column, -2.014 and 2.014 13. a. 80 10 8 i x x n Σ == = b. i x () i x x 2 i x x 10 0 0 8 -2 4 12 2 4 15 5 25 13 3 9 11 1 1 6 -4 16 5 -5 25 84 2 84 3.464 17 i xx s n Σ− = c. .025 ( / ) 2.365(3.464/ 8) 2.9 tsn d.
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Ch08 - Chapter 8 Interval Estimation Learning Objectives 1...

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