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solutions hw 8 - COMPREHENSIVE HOMEWORK PROBLEMS 1 a b c d...

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COMPREHENSIVE HOMEWORK PROBLEMS 1) In thinking about doing statistical analysis, the sample mean should be interpreted as: a) a constant value that is equal to the population mean. b) a constant value that is approximately equal to the population mean. c) a random variable that is approximately equal to the population mean when sampling is done without replacement. d) a random variable that is approximately equal to the population mean if n > 30 and when sampling is done without replacement. e)* a random variable that when averaged across many samples is approximately equal to the population mean. 2) Which of the following are random? x after a sample is taken ̄ x before a sample is taken ̄ µ after a sample is taken µ before a sample is taken More than one answer is correct. 3) a)* 3,000 and 26.8 $3,000 b) 3,000 and 1.69 26.80 c) 3,000 and 250 d) 3,000 and 2.87 e) 3,000 and 321.6 4) The following data was collected by taking a simple random sample of a population 13 15 14 16 12 From this we know that, The population mean is 14. 14 The point estimate of the population mean is 14. The population mean must be 14 since the sample mean is 14. Both a. and b. are correct. Both a., b., and c. are correct. 5) a) 0.0240 π = 0.07 b) 0.1428 n = 486 se(p) = √π(1 - π) ∕ n ̄ 0.0116 c) 0.4952 z = (p − π) ∕se(p) ̄ ̄ d)* 0.9904 2.59 P(-2.59 < z < 2.59) = 0.9904 e) None of the above answers is correct. 6) a) 0.0596 μ = 92 b) 0.0735 σ = 8 0.830 c) 0.4265 n = 93 d) 0.5596 z = -1.45 e)* 0.9265 P(z > -1.45) = 0.9265 7) Increasing the size of a sample from 100 to 200 will reduce the standard error of the mean to one-half its original value. have no effect on the standard error of the mean. n = 100 1 reduce the standard error of the mean to approximately 70% of its current value. n = 200 0.71 double the standard error of the mean. None of the above answers is correct. NEXT TWO ARE RELATED QUESTIONS ABOUT SAMPLING DISTRIBUTIONS. 8) a) increase. b)* decrease. c) remain approximately the same. d) change a lot, but not necessary increase or decrease. e) be similar to the variation of x values in the population. 9) a) remain unknown. b) to depend upon the population distribution of x. c) approximate the normal distribution, but not more closely than when 100 samples were drawn. d) less closely approximate the normal distribution. e)* more closely approximate the normal distribution. per CENTRAL LIMIT THEOREM. 10) a) $5 b) $7 381.00 c) $48 d) $242 e)* $381 11) a) 0.4013 b) 0.3783 P(x > 224) c) 0.352 d) 0.33 z = 0.25 e) 0.2643 P(z > 0.25) = 0.4013 12) a) 0.4483 μ = 220 b) 0.3446 σ = 16 1.789 c) 0.2148 n = 80 d)* 0.1314 z = 1.12 e) 0.1056 P(z > 1.12) = 0.1314 13) a) 205.98 to 234.02 MOE = 3.136 b) 210.08 to 229.92 216.86 c) 212.99 to 227.01 223.14 d) 215.57 to 224.43 e)* 216.86 to 223.14
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