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									172     Sampling Distributions

                CHAPTER 7: SAMPLING DISTRIBUTIONS

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

      ANSWER:
      b
      TYPE: 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:
      d
      TYPE: 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:
      c
      TYPE: MC DIFFICULTY: Difficult
      KEYWORDS: 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:
      a
      TYPE: MC DIFFICULTY: Moderate
      KEYWORDS: unbiased
                                                                       Sampling Distributions 173


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:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: 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  .
       d) The standard deviation of the sampling distribution of the sample mean is equal to  .

ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: 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  .
      b) The standard deviation of the sampling distribution is always  .
      c) The shape of the sampling distribution is always approximately normal.
      d) All of the above are true.

ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, properties
174     Sampling Distributions

      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:
      True
      TYPE: TF DIFFICULTY: Moderate
      KEYWORDS: 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:
      b
      TYPE: MC DIFFICULTY: Easy
      KEYWORDS: 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:
      d
      TYPE: MC DIFFICULTY: Moderate
      KEYWORDS: 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:
      biased
      TYPE: FI DIFFICULTY: Moderate
      KEYWORDS: 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:
      True
      TYPE: TF DIFFICULTY: Moderate
      KEYWORDS: central limit theorem
                                                                          Sampling Distributions 175


13. 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  = 6 ounces and  = 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:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: 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:
0.0228
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: 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 0
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: 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:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: sampling distribution, central limit theorem
176     Sampling Distributions

      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 0
              b) 0.2357
              c) 0.7357
              d) approximately 1

      ANSWER:
      d
      TYPE: MC DIFFICULTY: Moderate
      KEYWORDS: 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) 0.029
              b) 0.050
              c) 0.091
              d) 0.120

      ANSWER:
      a
      TYPE: MC DIFFICULTY: Easy
      KEYWORDS: 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:
      0.2710
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: 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?

      ANSWER:
      0.0416
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability
                                                                         Sampling Distributions 177


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:
1.057
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: 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) 0.003
       b) 0.050
       c) 0.200
       d) 0.800

ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: 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) 18.750
       b) 2.500
       c) 1.875
       d) 0.750

ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: 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) 0.0001
         b) 0.0013
         c) 0.0228
         d) 0.4987

ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
178     Sampling Distributions

      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:
      b
      TYPE: MC DIFFICULTY: Moderate
      KEYWORDS: 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:
      c
      TYPE: 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:
      b
      TYPE: 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:
      b
      TYPE: MC DIFFICULTY: Moderate
      KEYWORDS: standard error, mean
                                                                         Sampling Distributions 179


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:
d
TYPE: 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:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, central limit theorem

31. For sample size 1, the sampling distribution of the mean will be normally distributed
        a) 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:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, central limit theorem

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

ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standard error, proportion
180     Sampling Distributions


      33. True or False: As the sample size increases, the standard error of the mean increases.
      ANSWER:
      False
      TYPE: 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:
      True
      TYPE: 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:
      True
      TYPE: 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:
      False
      TYPE: 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:
      False
      TYPE: TF DIFFICULTY: Moderate
      EXPLANATION: The sample is too small for the normal approximation.
      KEYWORDS: sampling distribution, mean, probability
                                                                             Sampling Distributions 181



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:
True
TYPE: 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:
True
TYPE: 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:
True
TYPE: 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:
True
TYPE: 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:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution
182     Sampling Distributions


      43. True or False: Suppose  = 50 and  = 100 for a population. In a sample where n = 100 is
                                                 2

          randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

      ANSWER:
      True
      TYPE: TF DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability

      44. True or False: Suppose  = 80 and  = 400 for a population. In a sample where n = 100 is
                                                 2

          randomly taken, 95% of all possible sample means will fall above 76.71.

      ANSWER:
      True
      TYPE: TF DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability

      45. True or False: Suppose  = 50 and  = 100 for a population. In a sample where n = 100 is
                                                 2

          randomly taken, 90% of all possible sample means will fall between 49 and 51.

      ANSWER:
      False
      TYPE: TF DIFFICULTY: Moderate
      KEYWORDS: 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:
      True
      TYPE: TF DIFFICULTY: Easy
      KEYWORDS: 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:
      True
      TYPE: TF DIFFICULTY: Easy
      KEYWORDS: 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:
      False
      TYPE: TF DIFFICULTY: Easy
      KEYWORDS: sampling distribution
                                                                          Sampling Distributions 183



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:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: 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:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: 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:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, standard error

52. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with  = 110
    grams and  = 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:
0.9545
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability

53. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with  = 110
    grams and  = 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?

ANSWER:
0.0228
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability

54. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with  = 110
    grams and  = 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?

ANSWER:
0.9772
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
184     Sampling Distributions


      55. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with  = 110
          grams and  = 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:
      101.7757
      TYPE: PR DIFFICULTY: Difficult
      KEYWORDS: sampling distribution, mean, value

      56. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with  = 110
          grams and  = 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 115.2
      TYPE: 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 minutes
      TYPE: 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?

      ANSWER:
      0.4974
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability

      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?

      ANSWER:
      0.8767
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability
                                                                         Sampling Distributions 185



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 minutes
TYPE: 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 minutes
TYPE: 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:
True
TYPE: 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:
False
TYPE: 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:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, central limit theorem
186     Sampling Distributions


      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:
      0.3446
      TYPE: 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 __________.

      ANSWER:
      0.8849
      TYPE: FI DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability, central limit theorem

      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 __________.

      ANSWER:
      0.9836
      TYPE: FI DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability, central limit theorem

      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 __________.

      ANSWER:
      0.1891
      TYPE: FI DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability, central limit theorem

      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 ounces
      TYPE: FI DIFFICULTY: Difficult
      KEYWORDS: sampling distribution, mean, value, central limit theorem
                                                                        Sampling Distributions 187



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:
80
TYPE: 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:
5
TYPE: 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 __________.

ANSWER:
0.6554
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability, central limit theorem

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 __________.

ANSWER:
0.6898
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability, central limit theorem

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 __________.

ANSWER:
0.0548
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability, central limit theorem
188     Sampling Distributions

      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 minutes
      TYPE: 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: Easy
      KEYWORDS: sampling distribution, proportion, central limit theorem

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

      ANSWER:
      True
      TYPE: TF DIFFICULTY: Easy
      KEYWORDS: mean, unbiased

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

      ANSWER:
      True
      TYPE: TF DIFFICULTY: Difficult
      KEYWORDS: proportion, unbiased

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

      ANSWER:
      True
      TYPE: TF DIFFICULTY: Easy
      KEYWORDS: sampling distribution, proportion

      80. True or False: The standard error of the sampling distribution of a sample proportion is
            pS 1  pS 
                         where pS is the sample proportion.
                 n

      ANSWER:
      False
      TYPE: TF DIFFICULTY: Easy
      KEYWORDS: sampling distribution, proportion
                                                                           Sampling Distributions 189


81. True or False: The standard deviation of the sampling distribution of a sample proportion is
       p 1  p 
                  where p is the population proportion.
           n

ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: 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:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: standard error

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

ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: unbiased

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

ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: 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?

ANSWER:
0.3173
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
190     Sampling Distributions

      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?

      ANSWER:
      0.3085
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability

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

      ANSWER:
      0.2266
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability

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

      ANSWER:
      0.3829
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability

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

      ANSWER:
      0.4533
      TYPE: PR DIFFICULTY: Moderate
      KEYWORDS: sampling distribution, mean, probability

      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:
      0.9772
      TYPE: PR DIFFICULTY: Easy
      KEYWORDS: sampling distribution, mean, probability, central limit theorem
                                                                          Sampling Distributions 191


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

ANSWER:
0.5763
TYPE: PR DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, probability, central limit theorem

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

ANSWER:
0.3108
TYPE: PR DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, probability, central limit theorem

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

ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: 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:
0.8413
TYPE: PR DIFFICULTY: Easy
KEYWORDS: 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 hours
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
192     Sampling Distributions

      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 hours
      TYPE: PR DIFFICULTY: Difficult
      KEYWORDS: 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: Moderate
      KEYWORDS: 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:
      0.05050
      TYPE: FI DIFFICULTY: Moderate
      KEYWORDS: 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:
      True
      TYPE: TF DIFFICULTY: Easy
      KEYWORDS: 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:
      0.1596
      TYPE: PR DIFFICULTY: Easy
      KEYWORDS: 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: Easy
      KEYWORDS: sampling distribution, proportion, probability
                                                                           Sampling Distributions 193



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:
0.0015
TYPE: PR DIFFICULTY: Easy
KEYWORDS: sampling distribution, proportion, probability
103. 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:
21.47
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: 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:
8.528
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: 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: Moderate
KEYWORDS: 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:
0.05745
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: 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:
0.8034
TYPE: FI DIFFICULTY: Easy
KEYWORDS: sampling distribution, proportion, probability
194     Sampling Distributions

      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:
      0.1920
      TYPE: FI DIFFICULTY: Easy
      KEYWORDS: 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:
      49.83
      TYPE: FI DIFFICULTY: Difficult
      KEYWORDS: 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:
      35.55
      TYPE: FI DIFFICULTY: Difficult
      KEYWORDS: sampling distribution, proportion, value

								
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