Ch09 - CHAPTER9 SAMPLINGDISTRIBUTIONS...

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CHAPTER 9 SAMPLING DISTRIBUTIONS MULTIPLE CHOICE QUESTIONS In the following  multiple-choice questions, please circle the correct answer. 1. As   a   general   rule,   the   normal   distribution   is   used   to   approximate   the   sampling   distribution  of the sample proportion  only if a. the sample size  n  is greater than 30 b. the population  proportion   p  is close to 0.50 c. the underlying  population  is normal d. np  and   n (1- p ) are both greater than  5 ANSWER: d 2. Random  samples of size 49 are taken  from an infinite population  whose mean  is 300 and   standard  deviation  is 21. The mean  and  standard  error of the sample mean, respectively,   are: a. 300 and  21 b. 300 and  3 c. 70 and  230 d. 49 and  21 ANSWER: b 3. A normally  distributed  population  with  200 elements  has a mean  of 60 and  a standard   deviation  of 10. The probability that the mean  of a sample of 25 elements taken from this   population  will be smaller than 56 is a. 0.0166 b. 0.0228 c. 0.3708 d. 0.0394 139
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140 Chapter Nine ANSWER: a 4. Given  an  infinite  population  with  a  mean  of 75 and  a  standard  deviation  of 12, the   probability  that  the  mean  of a sample  of 36 observations,  taken  at  random  from  this   population, exceeds 78 is a. 0.4332 b. 0.0668 c. 0.0987 d. 0.9013 ANSWER: b 5. A   population   that   consists   of   500   observations   has   a   mean   of   40   and   a   standard   deviation  of 15. A  sample  of size  100 is taken  at  random  from  this  population.  The   standard  error of the sample mean  equals: a. 2.50 b. 12.50 c. 1.343 d. 1.50 ANSWER: c 6. An infinite population  has a mean  of 60 and  a standard  deviation  of 8. A sample  of 50  observations  will  be  taken  at  random  from  this  population.  The  probability  that  the   sample mean  will be between  57 and  62 is a. 0.9576 b. 0.9960 c. 0.2467 d. 0.3520 ANSWER: a 7. If all possible samples of size  n  are drawn  from  an infinite population  with  a mean  of 15  and  a standard  deviation  of 5, then  the  standard  error  of the  sample  mean  equals  1.0  only for samples of size a. 5 b. 15 c. 25 d. 75 ANSWER: c 8. If the standard  error  of the sampling  distribution  of the sample  proportion  is 0.0229 for   samples of size 400, then the population  proportion  must  be either a. 0.4 or 0.6 b. 0.5 or 0.5 c. 0.2 or 0.8 d. 0.3 or 0.7 ANSWER: d
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Sampling Distributions 141 9. As  a  general  rule  in  computing  the  standard  error  of  the  sample  mean,  the  finite   population  correction factor is used  only if the : a. sample size is smaller than  10% of the population  size b. population  size is smaller than  10% of the sample size
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Ch09 - CHAPTER9 SAMPLINGDISTRIBUTIONS...

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