# Quiz 7: Sampling and Sampling Distributions

Statistics

Q 1Q 1

From a group of 12 students, we want to select a random sample of 4 students to serve on a university committee. How many different random samples of 4 students can be selected?
A) 48
B) 20,736
C) 16
D) 495

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Multiple Choice

D

Q 2Q 2

Parameters are
A) numerical characteristics of a sample
B) numerical characteristics of a population
C) the averages taken from a sample
D) numerical characteristics of either a sample or a population

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B

Q 3Q 3

How many simple random samples of size 3 can be selected from a population of size 7?
A) 7
B) 21
C) 35
D) 343

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C

Q 4Q 4

Sampling distribution of is the
A) probability distribution of the sample mean
B) probability distribution of the sample proportion
C) mean of the sample
D) mean of the population

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Multiple Choice

Q 5Q 5

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12 respectively. The standard error of the mean is
A) 1.20
B) 0.12
C) 8.00
D) 0.80

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Multiple Choice

Q 6Q 6

A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within ± 2 of the population mean?
A) 0.6826
B) 0.3413
C) -0.6826
D) Since the mean is not given, there is no answer to this question.

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Multiple Choice

Q 7Q 7

The probability distribution of all possible values of the sample proportion is the
A) probability density function of
B) sampling distribution of
C) same as , since it considers all possible values of the sample proportion
D) sampling distribution of

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Multiple Choice

Q 8Q 8

In computing the standard error of the mean, the finite population correction factor is used when
A) N/n > 0.05
B) N/n ≤ 0.05
C) n/N > 0.05
D) n/N ≤ 30

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Multiple Choice

Q 9Q 9

Convenience sampling is an example of
A) probabilistic sampling
B) stratified sampling
C) nonprobabilistic sampling
D) cluster sampling

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Q 10Q 10

Which of the following is an example of nonprobabilistic sampling?
A) simple random sampling
B) stratified simple random sampling
C) cluster sampling
D) judgment sampling

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Multiple Choice

Q 11Q 11

Stratified random sampling is a method of selecting a sample in which
A) the sample is first divided into strata, and then random samples are taken from each stratum
B) various strata are selected from the sample
C) the population is first divided into strata, and then random samples are drawn from each stratum
D) None of these alternatives is correct.

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Multiple Choice

Q 12Q 12

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is
A) 0.100
B) 0.010
C) 0.001
D) 0.002

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Multiple Choice

Q 13Q 13

The closer the sample mean is to the population mean,
A) the larger the sampling error
B) the smaller the sampling error
C) the sampling error equals 1
D) None of these alternatives is correct.

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Multiple Choice

Q 14Q 14

Since the sample size is always smaller than the size of the population, the sample mean
A) must always be smaller than the population mean
B) must be larger than the population mean
C) must be equal to the population mean
D) can be smaller, larger, or equal to the population mean

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Multiple Choice

Q 15Q 15

As the sample size increases, the
A) standard deviation of the population decreases
B) population mean increases
C) standard error of the mean decreases
D) standard error of the mean increases

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Multiple Choice

Q 16Q 16

A simple random sample from an infinite population is a sample selected such that
A) each element is selected independently and from the same population
B) each element has a 0.5 probability of being selected
C) each element has a probability of at least 0.5 of being selected
D) the probability of being selected changes

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Multiple Choice

Q 17Q 17

A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is
A) 24
B) 56
C) 512
D) 128

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Multiple Choice

Q 18Q 18

In point estimation
A) data from the population is used to estimate the population parameter
B) data from the sample is used to estimate the population parameter
C) data from the sample is used to estimate the sample statistic
D) the mean of the population equals the mean of the sample

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Multiple Choice

Q 19Q 19

If we consider the simple random sampling process as an experiment, the sample mean is
A) always zero
B) always smaller than the population mean
C) a random variable
D) exactly equal to the population mean

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Q 20Q 20

The probability distribution of the sample mean is called the
A) central probability distribution
B) sampling distribution of the mean
C) random variation
D) standard error

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Q 21Q 21

The expected value of the random variable is
A) the standard error
B) the sample size
C) the size of the population
D) None of these alternatives is correct.

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Q 22Q 22

The standard deviation of all possible values is called the
A) standard error of proportion
B) standard error of the mean
C) mean deviation
D) central variation

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Q 23Q 23

A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The expected value of is
A) 8
B) 75
C) 800
D) None of these alternatives is correct.

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Multiple Choice

Q 24Q 24

As the sample size becomes larger, the sampling distribution of the sample mean approaches a
A) binomial distribution
B) Poisson distribution
C) normal distribution
D) chi-square distribution

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Multiple Choice

Q 25Q 25

Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for
A) only large sample sizes
B) only small sample sizes
C) any sample size
D) only samples of size thirty or greater

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Multiple Choice

Q 26Q 26

The sampling error is the
A) same as the standard error of the mean
B) difference between the value of the sample mean and the value of the population mean
C) error caused by selecting a bad sample
D) standard deviation multiplied by the sample size

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Multiple Choice

Q 27Q 27

The standard deviation of a sample of 100 elements taken from a very large population is determined to be 60. The variance of the population
A) can not be larger than 60
B) can not be larger than 3600
C) must be at least 100
D) can be any value greater or equal to zero

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Multiple Choice

Q 28Q 28

From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is
A) 3
B) 2
C) greater than 2
D) less than 2

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Multiple Choice

Q 29Q 29

The probability distribution of all possible values of the sample mean is
A) the probability density function of
B) the sampling distribution of
C) the grand mean, since it considers all possible values of the sample mean
D) one, since it considers all possible values of the sample mean

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Multiple Choice

Q 30Q 30

Which of the following sampling methods does not lead to probability samples?
A) stratified sampling
B) cluster sampling
C) systematic sampling
D) convenience sampling

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Q 32Q 32

A probability distribution for all possible values of a sample statistic is known as
A) a sample statistic
B) a parameter
C) simple random sampling
D) a sampling distribution

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Q 33Q 33

A population characteristic, such as a population mean, is called
A) a statistic
B) a parameter
C) a sample
D) the mean deviation

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Q 34Q 34

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is
A) 0.4332
B) 0.8664
C) 0.9332
D) 0.0668

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Multiple Choice

Q 35Q 35

A sample statistic, such as a sample mean, is known as
A) a statistic
B) a parameter
C) the mean deviation
D) the central limit theorem

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Q 36Q 36

The standard deviation of a point estimator is called the
A) standard deviation
B) standard error
C) point estimator
D) variance of estimation

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Q 37Q 37

A single numerical value used as an estimate of a population parameter is known as
A) a parameter
B) a population parameter
C) a mean estimator
D) a point estimate

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Multiple Choice

Q 38Q 38

The sample statistic, such as , s, or , that provides the point estimate of the population parameter is known as
A) a point estimator
B) a parameter
C) a population parameter
D) a population statistic

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Multiple Choice

Q 39Q 39

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the
A) approximation theorem
B) normal probability theorem
C) central limit theorem
D) central normality theorem

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Multiple Choice

Q 40Q 40

The purpose of statistical inference is to provide information about the
A) sample based upon information contained in the population
B) population based upon information contained in the sample
C) population based upon information contained in the population
D) mean of the sample based upon the mean of the population

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Multiple Choice

Q 41Q 41

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is
A) 1.875
B) 40
C) 5
D) 15

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Multiple Choice

Q 42Q 42

The number of random samples without replacement) of size 3 that can be drawn from a population of size 5 is
A) 15
B) 10
C) 20
D) 125

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Multiple Choice

Q 43Q 43

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are
A) 200 and 18
B) 81 and 18
C) 9 and 2
D) 200 and 2

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Multiple Choice

Q 44Q 44

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is
A) 0.5228
B) 0.9772
C) 0.4772
D) 0.0228

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Multiple Choice

Q 45Q 45

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the sample mean will be between 183 and 186 is
A) 0.1359
B) 0.8185
C) 0.3413
D) 0.4772

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Multiple Choice

Q 46Q 46

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3. The standard deviation of the sample proportions i.e., the standard error of the proportion) is
A) 0.0004
B) 0.2100
C) 0.3000
D) 0.0200

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Multiple Choice

Q 47Q 47

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is
A) 0.4332
B) 0.9332
C) 0.0668
D) 0.5668

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Multiple Choice

Q 48Q 48

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately
A) 1.1022
B) 2
C) 30
D) 1.4847

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Multiple Choice

Q 49Q 49

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have
A) the same probability of being selected
B) a probability of 1/n of being selected
C) a probability of 1/N of being selected
D) a probability of N/n of being selected

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Multiple Choice

Q 50Q 50

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is
A) 0.0016
B) 0.2400
C) 0.1600
D) 0.0400

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Multiple Choice

Q 51Q 51

For a population with any distribution, the form of the sampling distribution of the sample mean is
A) sometimes normal for all sample sizes
B) sometimes normal for large sample sizes
C) always normal for all sample sizes
D) always normal for large sample sizes

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Multiple Choice

Q 52Q 52

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a
A) population parameter
B) biased estimate of the population mean
C) sample parameter
D) point estimate

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Multiple Choice

Q 53Q 53

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 without replacement) which are possible equals
A) 12
B) 15
C) 3
D) 16

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Multiple Choice

Q 54Q 54

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. 12 18 19 20 21
A point estimate of the mean is
A) 400
B) 18
C) 20
D) 10

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Multiple Choice

Q 55Q 55

Random samples of size 36 are taken from an infinite population whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are
A) 36 and 15
B) 20 and 15
C) 20 and 0.417
D) 20 and 2.5

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Multiple Choice

Q 56Q 56

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is
A) approximately normal because is always approximately normally distributed
B) approximately normal because the sample size is large in comparison to the population size
C) approximately normal because of the central limit theorem
D) normal if the population is normally distributed

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Multiple Choice

Q 57Q 57

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately
A) normal because is always approximately normally distributed
B) normal because the sample size is small in comparison to the population size
C) normal because of the central limit theorem
D) None of these alternatives is correct.

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Multiple Choice

Q 58Q 58

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is
A) 0.0347
B) 0.7200
C) 0.9511
D) 8.3600

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Multiple Choice

Q 59Q 59

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is
A) 0
B) .0495
C) .4505
D) .9505

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Multiple Choice

Q 60Q 60

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are
A) 0.2 and .04
B) 0.2 and 0.2
C) 20 and .04
D) 20 and 0.2

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Multiple Choice

Q 61Q 61

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are
A) 500 and 0.047
B) 500 and 0.050
C) 0.5 and 0.047
D) 0.5 and 0.050

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Multiple Choice

Q 62Q 62

A sample of 25 observations is taken from an infinite population. The sampling distribution of is
A) not normal since n < 30
B) approximately normal because is always normally distributed
C) approximately normal if np ≥ 5 and n1-P) ≥ 5
D) approximately normal if np > 30 and n1-P) > 30

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Multiple Choice

Q 63Q 63

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is
A) 0.0568
B) 0.0778
C) 0.4222
D) 0.9222

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Multiple Choice

Q 64Q 64

A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is
A) 0.8633
B) 0.6900
C) 0.0819
D) 0.0345

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Multiple Choice

Q 65Q 65

A subset of a population selected to represent the population is
A) a subset
B) a sample
C) a small population
D) a parameter

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Multiple Choice

Q 66Q 66

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means
A) whenever the population is infinite
B) whenever the sample size is more than 5% of the population size
C) whenever the sample size is less than 5% of the population size
D) The correction factor is not necessary if the population has a normal distribution

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Multiple Choice

Q 67Q 67

Doubling the size of the sample will
A) reduce the standard error of the mean to one-half its current value
B) reduce the standard error of the mean to approximately 70% of its current value
C) have no effect on the standard error of the mean
D) double the standard error of the mean

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Multiple Choice

Q 68Q 68

The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the
A) central limit theorem
B) fact that we have tables of areas for the normal distribution
C) assumption that the population has a normal distribution
D) None of these alternatives is correct.

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Multiple Choice

Q 69Q 69

As the sample size increases, the variability among the sample means
A) increases
B) decreases
C) remains the same
D) depends upon the specific population being sampled

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Multiple Choice

Q 70Q 70

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever
A) np ≥ 5
B) n1 - p) ≥ 5 and n ≥ 30
C) n ≥ 30 and 1 - p) = 0.5
D) None of these alternatives is correct.

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Multiple Choice

Q 71Q 71

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are
A) 8.7 and 1.94
B) 36 and 1.94
C) 36 and 1.86
D) 36 and 8

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Multiple Choice

Q 72Q 72

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample mean for this situation?
A) approximately normal because the sample size is small relative to the population size
B) approximately normal because of the central limit theorem
C) exactly normal
D) None of these alternatives is correct.

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Multiple Choice

Q 73Q 73

The sampling distribution of the sample means
A) is the probability distribution showing all possible values of the sample mean
B) is used as a point estimator of the population mean μ
C) is an unbiased estimator
D) shows the distribution of all possible values of μ

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Multiple Choice

Q 74Q 74

Cluster sampling is
A) a nonprobability sampling method
B) the same as convenience sampling
C) a probability sampling method
D) None of these alternatives is correct.

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Multiple Choice

Q 75Q 75

The set of all elements of interest in a study is
A) set notation
B) a set of interest
C) a sample
D) a population

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Multiple Choice

Q 76Q 76

The number of different simple random samples of size 5 that can be selected from a population of size 8 is
A) 40
B) 336
C) 13
D) 56

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Multiple Choice

Q 77Q 77

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The point estimate of the population mean
A) cannot be determined, since the population size is unknown
B) is 14
C) is 4
D) is 5

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Multiple Choice

Q 78Q 78

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The point estimate of the population standard deviation is
A) 2.500
B) 1.581
C) 2.000
D) 1.414

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Multiple Choice

Q 79Q 79

The following data was collected from a simple random sample of a population. 13 15 14 16 12 If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?
A) 60
B) 210
C) 3024
D) 362880

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Multiple Choice

Q 80Q 80

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The mean of the population
A) is 14
B) is 15
C) is 15.1581
D) could be any value

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Multiple Choice

Q 81Q 81

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no." The point estimate of the proportion in the population who will respond "yes" is
A) 300
B) approximately 300
C) 0.75
D) 0.25

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Multiple Choice

Q 82Q 82

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no." The point estimate of the proportion in the population who will respond "no" is
A) 75
B) 0.25
C) 0.75
D) 0.50

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Multiple Choice

Q 83Q 83

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the mean of the population is
A) 18.0
B) 19.6
C) 108
D) sixteen, since 16 is the smallest value in the sample

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Multiple Choice

Q 84Q 84

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the population standard deviation is
A) 2.000
B) 1.291
C) 1.414
D) 1.667

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Multiple Choice

Q 85Q 85

How many different samples of size 3 can be taken from a finite population of size 10?
A) 30
B) 1,000
C) 720
D) 120

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Multiple Choice

Q 86Q 86

The sampling error is the
A) same as the standard error of the mean
B) difference between the value of the sample mean and the value of the sample proportion
C) error caused by selecting a bad sample
D) absolute value of the difference between the proportion of the population and proportion of the sample

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Multiple Choice

Q 87Q 87

Exhibit 7-1
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-1. The standard error of the mean equals
A) 0.3636
B) 0.0331
C) 0.0200
D) 4.000

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Multiple Choice

Q 88Q 88

Exhibit 7-1
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-1. The point estimate of the mean content of the bottles is
A) 0.22
B) 4
C) 121
D) 0.02

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Multiple Choice

Q 89Q 89

Exhibit 7-1
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-1. In this problem the 0.22 is
A) a parameter
B) a statistic
C) the standard error of the mean
D) the average content of colognes in the long run

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Multiple Choice

Q 90Q 90

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores.
-Refer to Exhibit 7-2. The point estimate for the mean of the population is
A) 750
B) 100
C) 85
D) 75

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Multiple Choice

Q 91Q 91

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores.
-Refer to Exhibit 7-2. The point estimate for the standard deviation of the population is
A) 419.43
B) 20.48
C) 75
D) 750

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Multiple Choice

Q 92Q 92

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores.
-Refer to Exhibit 7-2. The point estimate for the variance of the population is
A) 419.43
B) 20.48
C) 75
D) 750

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Multiple Choice

Q 93Q 93

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores.
-Refer to Exhibit 7-2. The point estimate for the proportion of all students who passed the course is
A) 0.8
B) 0.2
C) 1.8
D) 1.2

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Multiple Choice

Q 94Q 94

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The standard deviation of , known as the standard error of the proportion is approximately
A) 0.5477
B) 5.477
C) 0.05477
D) 54.77

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Multiple Choice

Q 95Q 95

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The probability that the sample proportion the proportion living in the dormitories) is between 0.30 and 0.50 is
A) 0.4664
B) 0.9328
C) 0.0336
D) 0.0672

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Multiple Choice

Q 96Q 96

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The probability that the sample proportion the proportion living in the dormitories) is at least 0.30 is
A) 0.4664
B) 0.9328
C) 0.9664
D) 0.0336

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Multiple Choice

Q 97Q 97

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.
a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean?
b. What is the probability that these 64 students will spend a combined total of more than $715.21?
c. What is the probability that these 64 students will spend a combined total between $703.59 and
$728.45?

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Essay

Q 98Q 98

A simple random sample of 6 recent graduates revealed the following information about their weekly incomes.
a. What is the expected value of the average weekly income of all the recent graduates?
b. What is the expected value of the standard deviation for the population?

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Essay

Q 99Q 99

The life expectancy in the United States is 75 with a standard deviation of 7 years. A random sample of 49 individuals is selected.
a. What is the probability that the sample mean will be larger than 77 years?
b. What is the probability that the sample mean will be less than 72.7 years?
c. What is the probability that the sample mean will be between 73.5 and 76 years?
d. What is the probability that the sample mean will be between 72 and 74 years?
e. What is the probability that the sample mean will be larger than 73.46 years?

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Essay

Q 100Q 100

The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected.
a. What is the probability that the sample mean will be larger than 1224?
b. What is the probability that the sample mean will be less than 1230?
c. What is the probability that the sample mean will be between 1200 and 1214?
d. What is the probability that the sample mean will be greater than 1200?
e. What is the probability that the sample mean will be larger than 73.46?

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Essay

Q 101Q 101

A simple random sample of 8 employees of a corporation provided the following information.
a. Determine the point estimate for the average age of all employees.
b. What is the point estimate for the standard deviation of the population?
c. Determine a point estimate for the proportion of all employees who are female.

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Essay

Q 102Q 102

An experimental diet to induce weight loss was followed for one week by a randomly selected group of 12 students with the following results.
a. Find a point estimate for the average amount lost after one week on this diet. Is this an unbiased estimate of the population mean? Explain.
b. Find a point estimate for the variance of the amount lost on this diet. Is this an unbiased estimate of the population variance? Explain.
c. Find a point estimate for the standard deviation of the amount lost on this diet.

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Essay

Q 103Q 103

MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500.
a. What are the expected value, the standard deviation, and the shape of the sampling distribution of ?
b. What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14?
c. What is the probability that the average aptitude test in the sample will be greater than 82.68?
d. What is the probability that the average aptitude test in the sample will be less than 78.69?
e. Find a value, C, such that P ≥ C) = .015.

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Essay

Q 104Q 104

Students of a large university spend an average of $5 a day on lunch. The standard deviation of the expenditure is
$3. A simple random sample of 36 students is taken.
a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean?
b. What is the probability that the sample mean will be at least $4?
c. What is the probability that the sample mean will be at least $5.90?

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Q 105Q 105

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken.
a. What are the expected value, standard deviation, and shape of the sampling distribution of ?
b. What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours?
c. What is the probability that the average life in the sample will be greater than 3,219.24 hours?
d. What is the probability that the average life in the sample will be less than 3,180.96 hours?

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Q 106Q 106

Michael is running for president. The proportion of voters who favor Michael is 0.8. A simple random sample of 100 voters is taken.
a. What are the expected value, standard deviation, and shape of the sampling distribution of ?
b. What is the probability that the number of voters in the sample who will not favor Michael will be between 26 and 30?
c. What is the probability that the number of voters in the sample who will not favor Michael will be more than 16?

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Q 107Q 107

In a restaurant, the proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of the restaurant is taken.
a. What are the expected value, standard deviation, and shape of the sampling distribution of ?
b. What is the probability that the proportion of people who will order coffee with their meal is between 0.85 and 0.875?
c. What is the probability that the proportion of people who will order coffee with their meal is at least 0.945?

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Q 108Q 108

A random sample of ten examination papers in a course that was given on a pass or fail basis showed the following scores.
a. What is the point estimate for the mean of the population?
b. What is the point estimate for the standard deviation of the population?
c. What is the point estimate for the proportion of all students who passed the course?

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Q 109Q 109

Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces.
a. Determine the mean and the variance of the population.
b. Sampling without replacement from the above population with a sample size of 2 produces ten possible samples. Using the ten sample mean values, determine the mean of the population and the variance of .
c. Compute the standard error of the mean.

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Q 110Q 110

The average weekly earnings of bus drivers in a city are $950 that is μ) with a standard deviation of $45 that is
σ). Assume that we select a random sample of 81 bus drivers.
a. Compute the standard error of the mean.
b. What is the probability that the sample mean will be greater than $960?
c. If the population of bus drivers consisted of 400 drivers, what would be the standard error of the mean?

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Q 111Q 111

An automotive repair shop has determined that the average service time on an automobile is 2 hours with a standard deviation of 32 minutes. A random sample of 64 services is selected.
a. What is the probability that the sample of 64 will have a mean service time greater than 114 minutes?
b. Assume the population consists of 400 services. Determine the standard error of the mean.

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Q 112Q 112

There are 8,000 students at the University of Tennessee at Chattanooga. The average age of all the students is 24 years with a standard deviation of 9 years. A random sample of 36 students is selected.
a. Determine the standard error of the mean.
b. What is the probability that the sample mean will be larger than 19.5?
c. What is the probability that the sample mean will be between 25.5 and 27 years?

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Q 113Q 113

In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study.
a. What is the probability that the sample proportion the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion the proportion living in the dormitories) is greater than 0.025?

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Q 114Q 114

A department store has determined that 25% of all their sales are credit sales. A random sample of 75 sales is selected.
a. What is the probability that the sample proportion will be greater than 0.34?
b. What is the probability that the sample proportion will be between 0.196 and 0.354?
c. What is the probability that the sample proportion will be less than 0.25?
d. What is the probability that the sample proportion will be less than 0.10?

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Q 115Q 115

Ten percent of the items produced by a machine are defective. A random sample of 100 items is selected and checked for defects.
a. Determine the standard error of the proportion.
b. What is the probability that the sample will contain more than 2.5% defective units?
c. What is the probability that the sample will contain more than 13% defective units?

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Q 116Q 116

There are 500 employees in a firm, 45% are female. A sample of 60 employees is selected randomly.
a. Determine the standard error of the proportion.
b. What is the probability that the sample proportion proportion of females) is between 0.40 and 0.55?

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Q 117Q 117

A new soft drink is being market tested. It is estimated that 60% of consumers will like the new drink. A sample of 96 taste tested the new drink.
a. Determine the standard error of the proportion
b. What is the probability that more than 70.4% of consumers will indicate they like the drink?
c. What is the probability that more than 30% of consumers will indicate they do not like the drink?

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Q 118Q 118

A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $300 with a standard deviation of $48. A random sample of 144 checking accounts is selected.
a. What is the probability that the sample mean will be more than $306.60?
b. What is the probability that the sample mean will be less than $308?
c. What is the probability that the sample mean will be between $302 and $308?
d. What is the probability that the sample mean will be at least $296?

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Q 119Q 119

In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded.
a. Compute the standard error of the proportion.
b. What is the probability that the sample contains at least 12 business majors?
c. What is the probability that the sample contains less than 15 business majors?
d. What is the probability that the sample contains between 12 and 14 business majors?

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Q 120Q 120

A simple random sample of 6 computer programmers in Houston, Texas revealed the sex of the programmers and the following information about their weekly incomes.
a. What is the point estimate for the average weekly income of all the computer programmers in Houston?
b. What is the point estimate for the standard deviation of the population?
c. Determine a point estimate for the proportion of all programmers in Houston who are female.

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Q 121Q 121

The milk prices in quarts) from a sample of 9 convenience stores in Chattanooga, Tennessee are shown below.
a. What is the point estimate for the prices of all convenience stores in Chattanooga?
b. What is the point estimate for the standard deviation of the population?

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Q 122Q 122

A random sample of 15 telephone calls in an office showed the duration of each call and whether it was a local or a long distance call.
a. What is the point estimate for the average duration of all calls?
b. What is the point estimate for the standard deviation of the population?
c. What is the point estimate for the proportion of all calls that were long distance?

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Q 123Q 123

An automotive repair shop has determined that the average service time on an automobile is 130 minutes with a standard deviation of 26 minutes. A random sample of 40 automotive services is selected.
a. Compute the standard error of the mean.
b. What is the probability that the sample of 40 automotive services will have a mean service time greater than 136 minutes?
c. Assume the population consists of 400 automotive services. Determine the standard error of the mean.

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Q 124Q 124

A department store has determined that 25% of all their sales are credit sales. A random sample of 60 sales is selected.
a. What is the sampling distribution of ?
b. What is the probability that the sample proportion will be greater than 0.30?
c. What is the probability that the sample proportion will be between 0.20 to 0.30?

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