CHAPTER 7: SAMPLING DISTRIBUTIONSs3.amazonaws.com/prealliance_oneclass_sample/a3AybxV0Vn.pdf · 175 Sampling Distributions KEYWORDS: central limit theorem 13. Suppose a sample of

172 Sampling Distributions

CHAPTER 7: SAMPLING DISTRIBUTIONS

1. Sampling distributions describe the distribution ofa) parameters.b) statistics.c) both parameters and statistics.d) neither parameters nor statistics.

ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: statistics, sampling distribution

2. The standard error of the mean a) is never larger than the standard deviation of the population.b) decreases as the sample size increases.c) measures the variability of the mean from sample to sample.d) all of the above

ANSWER:dTYPE: MC DIFFICULTY: Easy KEYWORDS: standard error, mean

3. The Central Limit Theorem is important in statistics because a) 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 sample size.c) for a large n, it says the sampling distribution of the sample mean is approximately

normal, regardless of the shape of the population.d) for any sized sample, it says the sampling distribution of the sample mean is

approximately normal.

ANSWER:cTYPE: MC DIFFICULTY: DifficultKEYWORDS: central limit theorem

4. If the expectation of a sampling distribution is located at the parameter it is estimating, then we call that statistic

a) unbiased.b) minimum variance.c) biased.d) random.

ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: unbiased


5. For air travelers, one of the biggest complaints involves the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.

a) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes.b) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8

minutes.d) Distribution is approximately normal with mean = 10 minutes and standard error = 8

minutes.

ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: central limit theorem

6. Which of the following statements about the sampling distribution of the sample mean is incorrect?

a) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n ≥ 30 ).

b) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means.

c) The mean of the sampling distribution of the sample mean is equal to µ .d) The standard deviation of the sampling distribution of the sample mean is equal to σ .

ANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: sampling distribution, properties

7. Which of the following is true about the sampling distribution of the sample mean?a) The mean of the sampling distribution is always µ .b) The standard deviation of the sampling distribution is always σ .c) The shape of the sampling distribution is always approximately normal.d) All of the above are true.

ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: sampling distribution, properties

Sampling Distributions 174

8. True or False: The amount of time it takes to complete an examination has a skewed-left distribution with a mean of 65 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 71 minutes is approximately 0.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: sampling distribution, central limit theorem

9. Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

a) The mean of the sample mean is equal to 23 years.b) The standard deviation of the sample mean is equal to 3 years.c) The shape of the sampling distribution is approximately normal.d) The standard error of the sample mean is equal to 0.3 years.

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: sampling distribution, central limit theorem

10. 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 normal.b) It allows us to disregard the shape of the sampling distribution when the size of the

population is large.c) It allows us to disregard the size of the population we are sampling from.d) It allows us to disregard the shape of the population when n is large.

ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: central limit theorem

11. A sample that does not provide a good representation of the population from which it was collected is referred to as a(n) sample.

ANSWER:biasedTYPE: FI DIFFICULTY: ModerateKEYWORDS: unbiased

12. True or False: 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:TrueTYPE: TF DIFFICULTY: Moderate


KEYWORDS: central limit theorem13. Suppose a sample of n = 50 items is 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 µ = 6 ounces and σ = 2.5 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 6 ounces.b) The standard deviation of the sampling distribution is 2.5 ounces.c) The shape of the sample distribution is approximately normal.d) All of the above are correct.

ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: sampling distribution, unbiased

14. The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 71.

ANSWER:0.0228TYPE: PR DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability, central limit theorem

15. The distribution of the number of loaves of bread sold per day by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 days has been selected. What is the approximate probability that the average number of loaves sold in the sampled days exceeds 7,895 loaves?

ANSWER:Approximately 0TYPE: PR DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability, central limit theorem

16. Sales prices of baseball cards from the 1960s are known to possess a skewed-right distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards.

a) Skewed-right with a mean of $5.25 and a standard error of $2.80.b) Normal with a mean of $5.25 and a standard error of $0.28.c) Skewed-right with a mean of $5.25 and a standard error of $0.28.d) Normal with a mean of $5.25 and a standard error of $2.80.

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: sampling distribution, central limit theorem


17. Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million.

a) approximately 0b) 0.2357c) 0.7357d) approximately 1

ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability, central limit theorem

18. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?

a) 0.029b) 0.050c) 0.091d) 0.120

ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: standard error, mean

19. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

ANSWER:0.2710TYPE: PR DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability

20. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be below 0.95 centimeters?



21. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means fall?

ANSWER:1.057TYPE: PR DIFFICULTY: DifficultKEYWORDS: sampling distribution, mean, value

22. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

a) 0.003b) 0.050c) 0.200d) 0.800

ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: standard error, mean

23. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and a 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 observation?

a) 18.750b) 2.500c) 1.875d) 0.750

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: sampling distribution, mean

24. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger?

a) 0.0001b) 0.0013c) 0.0228d) 0.4987

ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability


25. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

a) 84%b) 67%c) 29%d) 16%

ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability

26. The use of the finite population correction factor, when sampling without replacement from finite populations, will

a) increase the standard error of the mean.b) not affect the standard error of the mean.c) reduce the standard error of the mean.d) only affect the proportion, not the mean.

ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: finite population correction

27. For sample size 16, the sampling distribution of the mean will be approximately normally distributed

a) regardless of the shape of the population.b) if the shape of the population is symmetrical.c) if the sample standard deviation is known.d) if the sample is normally distributed.

ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, central limit theorem

28. The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would

a) increase the sample size to 200.b) increase the sample size to 400.c) decrease the sample size to 50.d) decrease the sample to 25.

ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, mean


29. 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 population.b) It has a normal distribution with the same mean and standard deviation as the population.c) It has the same shape and mean as the population, but has a smaller standard deviation.d) It has a normal distribution with the same mean as the population but with a smaller

standard deviation.

ANSWER:dTYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, central limit theorem

30. For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed

a) regardless of the shape of the population.b) only if the shape of the population is symmetrical.c) only if the standard deviation of the samples are known.d) only if the population is normally distributed.

ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem

31. For sample size 1, the sampling distribution of the mean will be normally distributeda) regardless of the shape of the population.b) only if the shape of the population is symmetrical.c) only if the population values are positive.d) only if the population is normally distributed.

ANSWER:dTYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, central limit theorem

32. The standard error of the proportion will become largera) as p approaches 0.b) as p approaches 0.50.c) as p approaches 1.00.d) as n increases.

ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, proportion


33. True or False: As the sample size increases, the standard error of the mean increases.ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: standard error, mean

34. True or False: If the population distribution is symmetric, the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 15 observations.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: population distribution, sampling distribution, mean, central limit theorem

35. True or False: 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:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem

36. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4, then 99.73% of all cars will purchase between $3 and $27.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability

37. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of $15 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 $13 and $17.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate EXPLANATION: The sample is too small for the normal approximation.KEYWORDS: sampling distribution, mean, probability


38. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4, and it is assumed that the amount of gasoline purchased per car is symmetric, there is approximately a 68.26% chance that a random sample of 16 cars will have a sample mean between $14 and $16.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability

39. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4, and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between $14 and $16.

ANSWER:TrueTYPE: TF DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, probability

40. True or False: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, law of large numbers

41. True or False: If the population distribution is skewed, 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:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem

42. True or False: A sampling distribution is a probability distribution for a statistic.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution


43. True or False: Suppose µ = 50 and σ 2 = 100 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability

44. True or False: Suppose µ = 80 and σ 2 = 400 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.71.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability

45. True or False: Suppose µ = 50 and σ 2 = 100 for a population. In a sample where n = 100 is randomly taken, 90% of all possible sample means will fall between 49 and 51.

ANSWER:FalseTYPE: TF DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability

46. True or False: The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches normal as the sample size increases.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: central limit theorem

47. True or False: The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: standard error, mean

48. True or False: A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

ANSWER:FalseTYPE: TF DIFFICULTY: EasyKEYWORDS: sampling distribution


49. True or False: As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

ANSWER:FalseTYPE: TF DIFFICULTY: EasyKEYWORDS: standard error, properties

50. True or False: For distributions such as the normal distribution, the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean

51. True or False: The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: sampling distribution, mean, standard error

52. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. What is the probability that the sample mean will be between 100 and 120 grams?

ANSWER:0.9545TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability

53. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. What is the probability that the sample mean will be less than 100 grams?


54. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. What is the probability that the sample mean will be greater than 100 grams?



55. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. So, 95% of all sample means will be greater than how many grams?

ANSWER:101.7757TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value

56. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. So, the middle 70% of all sample means will fall between what two values?

ANSWER:104.8 and 115.2TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value

57. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What would you expect the standard error of the mean to be?

ANSWER:2.5 minutesTYPE: PR DIFFICULTY: Easy KEYWORDS: standard error, mean

58. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean is between 45 and 52 minutes?


59. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?



60. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. So, 95% of all sample means will fall between what two values?

ANSWER:40.1 and 49.9 minutesTYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, probability

61. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. So, 90% of the sample means will be greater than what value?

ANSWER:41.8 minutesTYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, probability

62. True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean has a mean of 36.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, unbiased

63. True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. 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 0.15.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, standard error

64. True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. 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:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem


65. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample exceeds 36.01 oz. is __________.

ANSWER:0.3446TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem

66. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is less than 36.03 is __________.


67. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz. is __________.


68. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.95 and 35.98 oz. is __________.


69. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. So, 95% of the sample means based on samples of size 36 will be between __________ and __________.

ANSWER:35.951 ; 36.049 ouncesTYPE: FI DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value, central limit theorem


70. A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution of the sample mean is __________ minutes.

ANSWER:80TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, unbiased

71. A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The standard deviation of the sampling distribution of the sample mean is __________ minutes.

ANSWER:5TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, standard error

72. A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is __________.


73. A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be between 77 and 89 minutes is __________.


74. A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be greater than 88 minutes is __________.



75. A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. So, 95% of the sample means based on samples of size 64 will be between __________ and __________.

ANSWER:70.2 ; 89.8 minutesTYPE: FI DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value, central limit theorem

76. To use the normal distribution to approximate the binomial distribution, we need ______ and ______ to be at least 5.

ANSWER:np ; n(1-p)TYPE: FI DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion, central limit theorem

77. True or False: The sample mean is an unbiased estimate of the population mean.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: mean, unbiased

78. True or False: The sample proportion is an unbiased estimate of the population proportion.

ANSWER:TrueTYPE: TF DIFFICULTY: DifficultKEYWORDS: proportion, unbiased

79. True or False: The mean of the sampling distribution of a sample proportion is the population proportion, p.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion

80. True or False: The standard error of the sampling distribution of a sample proportion is

( )1S Sp p

n

− where Sp is the sample proportion.

ANSWER:FalseTYPE: TF DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion


81. True or False: The standard deviation of the sampling distribution of a sample proportion is

( )1p p

n

− where p is the population proportion.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion

82. True or False: A sample of size 25 provides a sample variance of 400. The standard error, in this case equal to 4, is best described as the estimate of the standard deviation of means calculated from samples of size 25.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: standard error

83. True or False: An unbiased estimator will have a value, on average across samples, equal to the population parameter value.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: unbiased

84. True or False: In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: mean, standard error

85. Assume that house prices in a neighborhood are normally distributed with a standard deviation of $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?



TABLE 7-1

Times spent studying by students in the week before final exams follow a normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.

86. Referring to Table 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?


87. Referring to Table 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?


88. Referring to Table 7-1, what is the probability that the sample mean differs from the population mean by less than 2 hours?


89. Referring to Table 7-1, what is the probability that the sample mean differs from the population mean by more than 3 hours?


TABLE 7-2

The mean selling price of new homes in a city over a 1-year period was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken.

90. Referring to Table 7-2, what is the probability that the sample mean selling price was more than $110,000?

ANSWER:0.9772TYPE: PR DIFFICULTY: EasyKEYWORDS: sampling distribution, mean, probability, central limit theorem


91. Referring to Table 7-2, what is the probability that the sample mean selling price was between $113,000 and $117,000?


92. Referring to Table 7-2, what is the probability that the sample mean selling price was between $114,000 and $116,000?


93. Referring to Table 7-2, without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie.

a) $113,000-$115,000b) $114,000-$116,000c) $115,000-$117,000d) $116,000-$118,000

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: sampling distribution, mean, probability, central limit theorem

TABLE 7-3

The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken.

94. Referring to Table 7-3, what is the probability that the sample mean lifetime is more than 1,550 hours?

ANSWER:0.8413TYPE: PR DIFFICULTY: EasyKEYWORDS: sampling distribution, mean, probability

95. Referring to Table 7-3, the probability is 0.15 that the sample mean lifetime is more than how many hours?

ANSWER:1,651.82 hoursTYPE: PR DIFFICULTY: ModerateKEYWORDS: sampling distribution, mean, probability


96. Referring to Table 7-3, the probability is 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?

ANSWER:64.08 hoursTYPE: PR DIFFICULTY: DifficultKEYWORDS: sampling distribution, mean, value

TABLE 7-4

According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected.

97. Referring to Table 7-4, the average of all the sample proportions of customers who will make a purchase after visiting the web site is _______.

ANSWER:0.15 or 15%TYPE: FI DIFFICULTY: ModerateKEYWORDS: sampling distribution, proportion, mean

98. Referring to Table 7-4, the standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

ANSWER:0.05050TYPE: FI DIFFICULTY: ModerateKEYWORDS: sampling distribution, proportion, standard error

99. True of False: Referring to Table 7-4, the requirements for using a normal distribution to approximate a binomial distribution are fulfilled.

ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion, central limit theorem

100. Referring to Table 7-4, what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

ANSWER:0.1596TYPE: PR DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion, probability

101. Referring to Table 7-4, what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

ANSWER:0.5


TYPE: PR DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion, probability

102. Referring to Table 7-4, what is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?

ANSWER:0.0015TYPE: PR DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion, probability103. Referring to Table 7-4, 90% of the samples will have less than what percentage of customers

who will make a purchase after visiting the web site?

ANSWER:21.47TYPE: PR DIFFICULTY: DifficultKEYWORDS: sampling distribution, proportion, value

104. Referring to Table 7-4, 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

ANSWER:8.528TYPE: PR DIFFICULTY: DifficultKEYWORDS: sampling distribution, proportion, value

105. A study at a college on the west coast reveals that, historically, 45% of their students are minority students. The expected percentage of minority students in their next batch of freshmen is _______.

ANSWER:45%TYPE: FI DIFFICULTY: ModerateKEYWORDS: sampling distribution, proportion, mean

106. A study at a college on the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, the standard error of the proportions of students in the samples who are minority students is _________.

ANSWER:0.05745TYPE: FI DIFFICULTY: ModerateKEYWORDS: sampling distribution, proportion, standard error

107. A study at a college on the west coast reveals that, historically, 45% of their students are minority students. If a random sample of size 75 is selected, the probability is _______ that between 30% and 50% of the students in the sample will be minority students.

ANSWER:0.8034TYPE: FI DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion, probability


108. A study at a college on the west coast reveals that, historically, 45% of their students are minority students. If a random sample of size 75 is selected, the probability is _______ that more than half of the students in the sample will be minority students.

ANSWER:0.1920TYPE: FI DIFFICULTY: EasyKEYWORDS: sampling distribution, proportion, probability

109. A study at a college on the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ______% of minority students.

ANSWER:49.83TYPE: FI DIFFICULTY: DifficultKEYWORDS: sampling distribution, proportion, value

110. A study at a college on the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 95% of the samples will have more than ______% of minority students.

ANSWER:35.55TYPE: FI DIFFICULTY: DifficultKEYWORDS: sampling distribution, proportion, value

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CHAPTER 7: SAMPLING DISTRIBUTIONSs3.amazonaws.com/prealliance_oneclass_sample/a3AybxV0Vn.pdf · 175 Sampling Distributions KEYWORDS: central limit theorem 13. Suppose a sample of