Sampling Distributions 315CHAPTER 9SAMPLING DISTRIBUTIONSSECTIONS 1 MULTIPLE CHOICE QUESTIONSIn 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 theoremb. standard error of the meanc. finite population correction factord. population standard deviationANSWER:b2.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 21b. 300 and 3c. 70 and 230d. 49 and 21ANSWER:b3.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 isa. 0.9576b. 0.9960c. 0.2467d. 0.3520ANSWER:a4.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 isa. 0.0166b. 0.0228c. 0.3708d. 0.0394ANSWER:a5.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 isa. 0.4332b. 0.0668c. 0.0987d. 0.9013ANSWER:b6.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. 2.50b. 12.50c. 1.343d. 1.50ANSWER:c7.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 sizea. 5b. 15c. 25d. 75ANSWER:c8.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 sizeb. population size is smaller than 10% of the sample sizec. sample size is greater than 1% of the population sized. population size is greater than 1% of the sample sizeANSWER:c9.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 isa. 0.9576b. 0.9960c. 0.2467d. 0.3520ANSWER:a10.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. 12.649b. 25.0c. 2.56d. 3.125ANSWER:d11.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 isa. 0.3970b. 0.4332c. 0.1469d. 0.0668ANSWER:c12.The finite population correction factor should not be used when:a. we are sampling from an infinite populationb. we are sampling from a finite populationc. sample size is greater than 1% of the population sized. None of the above ANSWER:a13.Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:a. 9 and 45b. 45 and 9c. 81 and 45d. 45 and 1ANSWER:d14.A sample of size 25 is selected at random from a finite population. If the finite population correction factor is 0.6325, then the population size is:a. 10b. 41c. 15d. 35ANSWER:b15.The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean :a. is approximately normal if n 30b. is approximately normal if n 30d. for all populationsANSWER:d18.If all possible samples of size n are dra