statistcs-9bykeller.doc

Sampling Distributions 319CHAPTER 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 drawn from an infinite population with a mean of and a standard deviation of , then the standard error of the sample mean is inversely proportional to:a.b.c. nd.ANSWER:d19.If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean will be:a. normal for all values of nb. normal only for n 30c. approximately normal for all values of nd. approximately normal only for n 30ANSWER:a20.If all possible samples of size n are drawn from a population, the probability distribution of the sample mean is called the:a. standard error ofb. expected value of c. sampling distribution of d. normal distributionANSWER: c21.Sampling distributions describe the distribution of a. population parametersb. sample statisticsc. both parameters and statisticsd. neither parameters nor statisticsANSWER:b22.The Central Limit Theorem is important in statistics becausea. for a large n, it says the population is approximately normal.b. for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the populationc. for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the populationd. for any sample size, it says the sampling distribution of the sample mean is approximately normalANSWER:c23.Which of the following statements about the sampling distribution of the sample mean is not true?a. The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n30)b. The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample meansc. The mean of the sampling distribution of the sample mean is equal to the population mean .d. The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation .ANSWER:d24.The standard error of the meana. is never larger than the standard deviation of the populationb. decreases as the sample size increasesc. measures the variability of the mean from sample to sampled. All of the aboveANSWER:d25.Which of the following is true about the sampling distribution of the sample mean?a. The mean of the sampling distribution is always equal to the population mean b. The standard deviation of the sampling distribution is always equal to the population standard deviation c. The shape of the sampling distribution is always approximately normald. All of the above are true.ANSWER:a26.The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and standard deviation of 0.8 pounds. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this sample mean?a. 6.800b. 2.500c. 0.128d. 0.720ANSWER:b27.Why is the Central Limit Theorem so important to the study of sampling distributions?a. It allows us to disregard the size of the sample selected when the population is not normalb. It allows us to disregard the shape of the sampling distribution when the size of the population is too largec. It allows us to disregard the size of the population we are sampling fromd. It allows us to disregard the shape of the population when the sample size n is largeANSWER:d28.Suppose that the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 15 computer chips is taken. What is the standard error for the sample mean?a. 0.0258b. 0.0067c. 0.0026d. 0.1500ANSWER:a29.The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and standard deviation of 0.84 pounds. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?a. 0.200b. 0.053c. 0.210d. 0.800ANSWER:c30.Suppose the ages of students in your university or college follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is not true?a. The mean of the sampling distribution of sample mean is equal to 24 yearsb. The standard deviation of the sampling distribution of sample mean is equal to 4 yearsc. The shape of the sampling distribution of sample mean is approximately normald. None of the aboveANSWER:b31.Suppose that items are drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with = 8 ounces and = 3 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?a. The mean of the sampling distribution is 3 ouncesb. The standard deviation of the sampling distribution is 3 ouncesc. The shape of the sampling distribution is approximately normald. All of the above are correctANSWER:a32.The standard error of the mean for a sample of 100 is 25. In order to cut the standard error of the mean to 12.5, we woulda. increase the sample size to 200b. increase the sample size to 400c. decrease the sample size to 50d. decrease the sample to 25ANSWER:b33.Which of the following is true regarding the sampling distribution of the mean for a large sample size?a. It has the same shape, mean and standard deviation as the populationb. It has a normal distribution with the same mean and standard deviation as the populationc. It has the same shape and mean as the population, but has a smaller standard deviationd. It has a normal distribution with the same mean as the population but with a smaller standard deviationANSWER:d34.For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributeda. regardless of the shape of the populationb. only if the shape of the population is symmetricalc. only if the standard deviation of the samples are knownd. only if the population is normally distributedANSWER:a35.For a sample size of 1, the sampling distribution of the mean will be normally distributed a. regardless of the shape of the populationb. only if the shape of the population is positively skewedc. only if the population values are larger than 30d. only if the population is normally distributedANSWER:dTRUE / FALSE QUESTIONS36.When a great many simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal regardless of sample size n.ANSWER:T37.The central limit theorem is basic to the concept of statistical inference, because it permits us to draw conclusions about the population based strictly on sample data, and without having any knowledge about the distribution of the underlying population.ANSWER:T 38.The standard error of the mean is the standard deviation of the sampling distribution of the sample mean .ANSWER:T39.The standard deviation of the sampling distribution of the sample mean is also called the point estimate of the population standard deviation.ANSWER:F40.Consider an infinite population with a mean of 100 and a standard deviation of 20. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals 2.5.ANSWER:T41.If all possible samples of size n are drawn from an infinite population with a mean of 60 and a standard deviation of 8, then the standard error of the sample mean equals 1.0 only for samples of size 64.ANSWER:T42.A sample of size n is selected at random from an infinite population. As n increases, the standard error of the sample mean increases.ANSWER:F43.A sample of size 25 is selected at random from a finite population. If the finite population correction factor is 0.822, the population size must be 75.ANSWER:T44.The amount of time it takes to complete a final examination is negatively skewed distribution with a mean of 70 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 76 minutes is approximately 0.ANSWER:T45.The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean and standard deviation are known.ANSWER:T46.If all possible samples of size n are drawn from a population, the probability distribution of the sample mean is referred to as the normal distribution. ANSWER:F47.If the sample size increases, the standard error of the mean remains unchanged.ANSWER:F48.The amount of bleach a machine pours into bottles has a mean of 50 ounces with a standard deviation of 0.25 ounces. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean has a mean of 50 ounces.ANSWER:T49.If the amount of gasoline purchased per car at a gas station has population mean of $16 and a population standard deviation of $4 and a random sample of 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be between $14 and $18.ANSWER:F50.If the population distribution is skewed, in most cases the sampling distribution of the sample mean can be approximated by the normal distribution if the samples contain at least 30 observations.ANSWER:T51.A sampling distribution is a probability distribution for a statistic.ANSWER:T52.The amount of bleach a machine pours into bottles has a mean of 50 ounces with a standard deviation of 0.25 ounces. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean will be approximately normal only if the population sampled is normal.ANSWER:F53.A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.ANSWER:F54.If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.ANSWER:T55.The amount of bleach a machine pours into bottles has a mean of 50 ounces with a standard deviation of 0.25 ounces. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean has a standard error of 0.25 ounces.ANSWER:F56.If the amount of gasoline purchased per car at a gas station has a population mean of $16 and a population standard deviation of $4, then 99.4% of all cars will purchase between $4 and $28 worth of gasoline.ANSWER:F57.As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population decrease.ANSWER:T58.A sample size of 25 provides a sample standard deviation of 20. The standard error, in this case equals to 4, is best described as the estimate of the standard deviation of means calculated from samples of size 25.ANSWER:T59.In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.ANSWER:TSTATISTICAL CONCEPTS & APPLIED QUESTIONSFOR QUESTIONS 60 THROUGH 62, USE THE FOLLOWING NARRATIVE:Narrative: Reading BooksA researcher conducted a survey on a university campus for a sample of 64 seniors and reported that seniors read an average of 3.12 books in the prior academic semester, with a standard deviation of 2.15 books. 60.Reading Books Narrative Determine the probability that the sample mean is above 3.45 books.ANSWER:0.109361.Reading Books Narrative Determine the probability that the sample mean is between 3.38 and 3.58 books.ANSWER:0.122462.Reading Books Narrative Determine the probability that the sample mean is below 2.94 books.ANSWER:0.251463.An infinite population has a mean of 150 and a standard deviation of 40. A sample of 100 observations will be selected at random from the population.a. What is the expected value of the sample mean?b. What is the standard deviation of the sample mean?c. What is the shape of the sampling distribution of the sample meand. What does the sampling distribution of the sample mean show?ANSWER:a. =150b. = 4c. Approximately normal with a mean of 150 and a standard deviation of 4.d. It shows the probability distribution of all possib