Mathematics
Can you do chapter 8?

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I’m studying for my Statistics class and need an explanation.

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8. a. Since n is small, an assumption that the population is at least approximately normal is required so that the sampling distribution of x can be approximated by a normal distribution. b. Margin of error: z.025 ( / n ) = 1.96(5.5 / 10) = 3.41 c. Margin of error: z.005 ( / n ) = 2.576(5.5 / 10) = 4.48 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 x  t / 2 (s / n ) 15. 90% confidence df = 64 t.05 = 1.669 19.5 ± 1.669 (5.2 / 65) 19.5 ± 1.08 or 18.42 to 20.58 95% confidence df = 64 19.5 ± 1.998 (5.2 / 65) 19. t.025 = 2.015 t.025 = 1.998 a. t.025 (s / n ) df = 44 s = 65 2.015 (65 / 45) = 19.52 or approximately \$20 b. x  t.025 (s / n ) 273 ± 20 or 253 to 293 c. At 95% confidence, the population mean is between \$253 and \$293. This is definitely above the \$229 level of 2 years ago. Hotel room rates are increasing. The point estimate of the increase is \$273 - \$229 = \$44 or 19%. 19.5 ± 1.29 or 18.21 to 20.79 19. a. t.025 (s / n ) df = 44 t.025 = 2.015 s = 65 2.015 (65 / 45) = 19.52 or approximately \$20 b. x  t.025 (s / n ) 273 ± 20 or 253 to 293 c. At 95% confidence, the population mean is between \$253 and \$293. This is definitely above the \$229 level of 2 years ago. Hotel room rates are increasing. The point estimate of the increase is \$273 - \$229 = \$44 or 19%. 26. a. n= 2 z.025  2 (1.96) 2 (.25) 2 = = 24.01 Use 25. E2 (.10) 2 If the normality assumption for the population appears questionable, this should be adjusted upward to at least 30. b. c. (1.96) 2 (.25) 2 = 49 Use 49 to guarantee a margin of error no greater than .07. However, the US (.07) 2 EIA may choose to increase the sample size to a round number of 50 n= n= (1.96) 2 (.25) 2 = 96.04 Use 97 (.05) 2 For reporting purposes, the US EIA might decide to round up to a sample size of 100. 39. a. n= 2 z.025 p (1 − p ) (1.96) 2 (.156)(1 − .156) = = 562 E2 (.03) 2 b. n= 2 z.005 p (1 − p ) (2.576) 2 (.156)(1 − .156) = = 970.77 Use 971 E2 (.03) 2 ...
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