Deck 7: Sampling Distributions

Question 1

What is the term for a numerical descriptive measure calculated from the entire population?

A) a parameter
B) a statistic
C) a sample
D) a sampling distribution

Answer 1

A

Question 2

If all possible samples of size n are drawn from a large population with a mean of 20 and a standard deviation of 5, then for which of the following samples sizes would the standard error of the sample mean equal 1.0?

A) 15
B) 20
C) 25
D) 30

Answer 2

C

Question 3

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the probability that the mean score of a sample of 64 students is at least 80?

A) 0.0987
B) 0.4772
C) 0.5987
D) 0.9772

Answer 3

D

Question 4

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the standard deviation of the sampling distribution of the sample mean, , if a sample of 64 students is selected at random from all students taking that course?

A) 10.25
B) 8.00
C) 1.25
D) 1.00

Question 5

If all possible samples of size n are drawn from a large population with a mean of and a standard deviation of , then the standard error of the sample mean is inversely proportional to which of the values listed below?

A)
B)
C) n
D)

Question 6

Given a sampling distribution of the sample mean, , that is normally distributed and has a mean of 30 and a standard deviation of 8, to which of the following does a sample mean of 40 correspond?

A) a z value of -1.25
B) a z value of +1.25
C) a sample size of 120
D) a sample size of 300

Question 7

Which of the following is a commonly used parameter?

A) the sample mean,
B) the standard deviation, s
C) the standard deviation,
D) the sample meanand the standard deviation, s

Question 8

When a sample is selected at random from a population, which of the following will probably be the case?

A) The sample mean,, will likely be larger than the population mean.
B) The sample mean,, will likely be smaller than the population mean.
C) The sample mean,, will likely be different from the population mean.
D) The sample mean,, will likely be equal to the population mean.

Question 9

Consider a large population with a mean of 150 and a standard deviation of 27. A random sample of size 36 is taken from this population. Which of these values is equal to the standard error of the sampling distribution of sample mean?

A) 4.17
B) 4.50
C) 5.20
D) 5.56

Question 10

Which of the following is the standard error of a statistic used as an estimator of a population parameter?

A) the standard deviation of the sampling distribution of the statistic
B) the variance of the sampling distribution of the statistic
C) the same value as the population standard deviation
D) the same value as the population variance

Question 11

Random samples of size 36 each are taken from a large population whose mean is 120 and standard deviation is 39. In this case, which of the following are the values of the mean and the standard error, respectively, of the sampling distribution of the sample mean?

A) 120 and 39
B) 120 and 6.5
C) 39 and 120
D) 6.5 and 120

Question 12

Given N = 1000, n = 30, and = 6, what is the standard error of the sample mean, SE ?

A) 0.009
B) 0.5
C) 1.095
D) 33.33

Question 13

Suppose the monthly rents of all one-bedroom apartments in a small town are known to be normally distributed with a mean equal to $175 a month and standard deviation of $35. Which of the following would be the highest individual rent that you might expect to find?

A) about $210
B) about $280
C) about $4245
D) more information is needed to answer the question

Question 14

Which of the following does NOT correctly describe a random sample?

A) It is a subset of the population of interest.
B) Its summary measures are called parameters.
C) Its summary measures are called statistics.
D) Each of the elements in it has the same likelihood of being selected.

Question 15

Given a population variance of = 36 and a sample size of n = 9, which of the following would equal the standard deviation of the sampling distribution of the sample mean, ?

A) 4
B) 2
C) 1/2
D) 1/4

Question 16

Suppose that 20% of the households in Alberta have incomes in excess of $60,000. Assume that a random sample of 500 households in Alberta is taken. What will be the standard error of the sampling distribution of sample proportion of households that have incomes in excess of $60,000?

A) 0.0003
B) 0.0179
C) 0.0256
D) 0.1600

Question 17

When drawing all possible simple random samples of a given size n from a population, many different values of a sample statistic might occur. What is the term for a listing of all these possible values, along with the associated probabilities of their occurrence?

A) the statistic's finite population correction factor
B) the statistic's probability density function
C) the statistic's sampling distribution
D) the statistic's standard normal deviate

Question 18

What is the term for a numerical descriptive measure calculated from a sample?

A) a parameter
B) a statistic
C) a population
D) a sampling distribution

Question 19

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the mean of the sampling distribution of the sample mean, , if a sample of 64 students is selected at random from all students taking that course?

A) 64
B) between 74 and 90
C) between 78 and 86
D) 82

Question 20

Which of the sample sizes below will produce a sampling distribution of the mean that is approximately normal?

A) 10
B) 20
C) 30
D) 35

Question 21

Which of the following is another name for assignable cause variation?

A) random variation
B) special cause variation
C) common cause variation
D) controlled variation

Question 22

The spread of the distribution of sample means is considerably less than the spread of the sampled population.

Question 23

If random samples of size n = 36 are drawn from a non-normal population with finite mean = 75 and standard deviation = 15, then the sampling distribution of the sample mean is approximately normally distributed with mean = 75 and standard deviation = 2.5.

Question 24

For a control chart, where are the lower and upper control limits usually set?

A) one standard deviation from the centreline
B) two standard deviations from the centreline
C) three standard deviations from the centreline
D) four standard deviations from the centreline

Question 25

According to the Central Limit Theorem, for large samples, the standard error of the sample mean is the population standard deviation divided by the square root of the sample size.

Question 26

If the standard error of the sampling distribution of the sample proportion is 0.02049 for samples of size 500, then what may we conclude about the population proportion?

A) The population proportion must be either 0.2 or 0.8.
B) The population proportion must be either 0.5 or 0.5.
C) The population proportion must be either 0.3 or 0.7.
D) The population proportion must be either 0.6 or 0.4.

Question 27

What are some of the most common sources of random variation?

A) people
B) materials
C) neither people nor materials
D) both people and materials

Question 28

As a general rule, the normal distribution provides a good approximation to the sampling distribution of the sample proportion, , only if which of the following conditions holds?

A) The sample size, n, is greater than 30.
B) The population proportion, p, is greater than 0.50.
C) The underlying population has a small standard deviation and n is large.
D) np and n(1 - p) are both greater than 5.

Question 29

Given a population proportion of p = 0.8 and a sample size of n = 100, what is the standard deviation of the sampling distribution of the sample proportion, ?

A) 0.0258
B) 0.0355
C) 0.0400
D) 0.4000

Question 30

The Central Limit Theorem does not apply to the sample means of large samples drawn from a discrete distribution.

Question 31

Twenty-five samples of size 1000 each were drawn from a manufacturing process and the number of defectives in each sample was counted. The average sample proportion was 0.05. What would be the upper control limit for the p chart?

A) 0.0206
B) 0.0293
C) 0.0475
D) 0.0707

Question 32

The most important contribution of the Central Limit Theorem is in statistical inference.

Question 33

If random samples of size n = 50 are drawn from a non-normal population with finite mean = 100 and standard deviation = 20, then the sampling distribution of the sum of sample measurements is approximately normally distributed with mean = 5000 and standard deviation = 1000.

Question 34

In a recent study, it was reported that the proportion of employees who miss work on Fridays is 0.15, and that the standard deviation of the sampling distribution of sample proportion, , is 0.025. What was the sample size, n?

A) 204
B) 108
C) 26
D) 87

Question 35

Sixty samples of size 600 each were drawn from a manufacturing process and the number of defectives in each sample was counted. The average sample proportion was 0.04. What would be the lower control limit for the p chart?

A) 0.008
B) 0.016
C) 0.048
D) 0.064

Question 36

The sampling distribution of the sample mean is exactly normally distributed, regardless of the sample size n.

Question 37

The mean of the sample means and the standard deviation of 50 samples of size 5 taken from a production process under control are found to be 300 and 25, respectively. At which of the following values would the lower control limit for the chart be located?

A) 333.54
B) 310.61
C) 289.39
D) 266.46

Question 38

A statistics professor has stated that 90% of his students pass the class. To check this claim, a random sample of 150 students indicated that 129 passed the class. If the professor's claim is correct, what is the probability that 129 or fewer will pass the class this semester?

A) 0.9484
B) 0.5516
C) 0.4484
D) 0.0516

Question 39

Fifty samples of size 500 were drawn from a manufacturing process and the number of defectives in each sample was counted. The average of the sample proportion was 0.032. At which of the following values would the centreline for the p chart be located?

A) 0.032
B) 0.512
C) 0.968
D) 16.0

Question 40

The Central Limit Theorem describes the distribution of the sample mean except for populations that are normal.

Question 41

A sampling distribution is a probability distribution that shows the likelihood of occurrence associated with all the possible values of a parameter whose values would be obtained when drawing all possible samples of a given size from a population.

Question 42

The population of pop cans filled by a particular machine is known to be normally distributed with a mean of 12 ounces and a standard deviation of 0.16 ounces. Given this information, the sampling distribution of the sample mean, , for a random sample of 16 cans will also be normally distributed with a standard deviation equal to 0.04.

Question 43

In practical business situations, it is very unlikely that a decision maker will actually construct a sampling distribution of any kind.

Question 44

A sampling distribution is defined as a sample chosen in such a way that every possible subset of like size has an equal chance of being selected.

Question 45

The sample standard deviation measures the variability of all possible sample mean, , values that might be obtained.

Question 46

According to the Central Limit Theorem, any sampling distribution of the sample proportion will be normal provided np < 5, while .

Question 47

A sampling distribution is the distribution of the values that are included in a sample selected randomly from the population.

Question 48

The population of pop cans filled by a particular machine is known to be normally distributed with a mean of 340 mL and a standard deviation of 4.5 mL. Given this information, the sampling distribution of the sample mean, , for a random sample of 16 cans will also be normally distributed with a mean equal to

Question 49

The mean for a sample selected randomly from a population is most likely to be lower or higher than the known value of the population mean.

Question 50

The total area under a probability density function curve is equal to 1.0.

Question 51

As the sample size increases, the standard error of the sample mean decreases.

Question 52

The sampling distribution of the sample mean, , is the distribution of all possible sample means that could be computed from all possible samples of a given size, n.

Question 53

If a population standard deviation is equal to 50, then the sampling distribution of the sample mean, , will have a standard deviation that is less than 50 for all samples of size n > 2.

Question 54

If is the mean of a simple random sample taken from a large population, and if the N population values are normally distributed, the sampling distribution of is also normally distributed, regardless of sample size, n.

Question 55

The mean of the sampling distribution of sample mean, , is equal to the mean of the population from which the samples are selected to construct the sampling distribution.

Question 56

A summary measure calculated for a population is called a parameter and is designated by Greek letters (such as for mean or for proportion).

Question 57

If a population standard deviation is equal to 24.8, then the sampling distribution of the sample mean, , will have a standard deviation that is less than 24.8 for all possible sample sizes.

Question 58

According to the Central Limit Theorem, any sampling distribution of is considered normal, provided .

Question 59

When all possible simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal, regardless of sample size, n.

Question 60

The standard deviation of a statistic that is used to estimate an unknown parameter is called the standard error of the statistic.

Question 61

According to the Central Limit Theorem, if is the mean of a simple random sample taken from a large population, and if the N population values are normally distributed, the sampling distribution of is also normally distributed, regardless of sample size, n.

Question 62

Recall the rule of thumb used to indicate when the normal distribution is a good approximation of the sampling distribution for the sample proportion, . For the combination n = 25, p = 0.05; the rule is satisfied.

Question 63

Standard error of the sample proportion is another term for the variance of the sampling distribution of the sample proportion, .

Question 64

The standard error of the sampling distribution of the sample proportion, , when n = 100 and p = 0.15 is 0.001275.

Question 65

According to the Central Limit Theorem, if is the mean of a simple random sample taken from a large population, and if the N population values are not normally distributed, the sampling distribution of nevertheless approaches a normal distribution when n 30 and also n < 0.05N, because these values make the approximation almost perfect.

Question 66

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if the sample size, n, is greater than or equal to 30.

Question 67

The Central Limit Theorem is used to describe the sampling distributions of statistics, such as and , when the population is known to be normally distributed.

Question 68

In order to use the Central Limit Theorem to describe the sampling distribution of the sample mean, , the sample size, n, must be 30 or more.

Question 69

According to the Central Limit Theorem, if is the mean of a simple random sample taken from a large population, and if the N population values are not normally distributed, the sampling distribution of nevertheless approaches a normal distribution as sample size, n, increases.

Question 70

The Central Limit Theorem applies to the sampling distribution of sample proportion, , but not to the sampling distribution of sample mean, .

Question 71

A population with a large standard deviation will have a sampling distribution that is more spread out for a given sample size than a similar population with a small standard deviation.

Question 72

The Central Limit Theorem states that the sampling distribution of the population mean, , is approximately normal, provided that .

Question 73

The Central Limit Theorem states that the sample mean, , is equal to the population mean, , provided that .

Question 74

The expression SE represents the standard error sampling distribution of the sample proportion, .

Question 75

The population of incomes in a community college in Ontario is thought to be highly skewed to the right with a mean equal to $38,765 and a standard deviation equal to $2,640. Based on this information, if a sample of size 36 is selected at random, then the highest sample mean that we would expect to see would be approximately $40,085.

Question 76

The mean of the sampling distribution of the sample proportion, , when n = 100 and p = 0.5 is 5.0.

Question 77

As the sample size increases, the standard error of the sample proportion decreases.

Question 78

The expression SE represents the standard deviation of the sampling distribution of the sample proportion, .

Question 79

The Central Limit Theorem states that the sample mean, , is always equal to the population mean, .

Question 80

The Central Limit Theorem states that the sampling distribution of the sample mean, , is approximately normal for large sample sizes ( ).