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CHAPTER 9 SAMPLING DISTRIBUTIONS SECTIONS 1 MULTIPLE CHOICE QUESTIONS In the following multiple-choice questions, please circle the correct answer. 1. The standard deviation of the sampling distribution of the sample mean is also called the: a. central limit theorem b. standard error of the mean c. finite population correction factor d. population standard deviation ANSWER: b 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. 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 29 30 Chapter Nine a. 0.9576 b. 0.9960 c. 0.2467 d. 0.3520 ANSWER: a 4. 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 ANSWER: a 5. 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 6. 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 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. 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 c. sample size is greater than 1% of the population size Sampling Distributions 31 d. population size is greater than 1% of the sample size ANSWER: c 9. 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 10. Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals: a. 12.649 b. 25.0 c. 2.56 d. 3.125 ANSWER: d 11. A sample of size 40 will be taken from an infinite population whose mean and standard deviation are 68 and 12, respectively. The probability that the sample mean will be larger than 70 is... View Full Document