Deck 8: Sampling Methods and the Central Limit Theorem

Question 1

In stratified random sampling,a population is divided into strata using naturally occurring geographic or other boundaries. Then,strata are randomly selected and a random sample is collected from each strata.

Answer 1

False

Question 2

When using stratified random sampling,the sampling error will be zero.

Answer 2

False

Question 3

The mean of all possible sample means is equal to the population mean.

Answer 3

True

Question 4

If the sampling distribution of the sample means approximates a normal distribution,then the population must be normally distributed.

Question 5

When doing research,knowing the population mean and other population parameters is essential.

Question 6

It is often not feasible to study the entire population because it is impossible to observe all the items in the population.

Question 7

If the size of a sample equals the size of the population,we would not expect any error in estimating the population parameter.

Question 8

If 40 samples of size 21 were selected from a population of 22,493,we would expect the mean of the sample means and the population mean to be close but not exactly equal.

Question 9

Based on the central limit theorem,the sample mean can be used as a good estimator of the population mean,assuming that the size of the sample is sufficiently large.

Question 10

Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.

Question 11

The items or individuals of the population are arranged in a file drawer alphabetically by date received. A random starting point is selected and then every kth member of the population is selected for the sample. This sampling method is called systematic random sampling.

Question 12

In the sampling distribution of the sample means,the standard error of the mean will vary according to the size of the sample. As the sample size,n,gets larger,the variability of the sampling distribution of the means gets larger.

Question 13

In cluster sampling,a population is divided into subgroups called clusters,and a sample is randomly selected from each cluster.

Question 14

We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.

Question 15

The standard error of the mean is also called the sampling error.

Question 16

For the sampling distribution of sample means,standard error will decrease as sample size increases.

Question 17

The central limit theorem states that for a sufficiently large sample,the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to σ² and the variance equal to σ²/n.

Question 18

A sampling distribution of the means is a probability distribution consisting of all possible sample means of a given sample size selected from a population.

Question 19

The central limit theorem states that if the sample size,n,is sufficiently large,the sampling distribution of the means will be approximately normal,even when the population is skewed or uniform.

Question 20

When deciding to collect sample information rather than collecting information from the population,the amount of time required to collect the information is unimportant.

Question 21

When testing the safety of cars using crash tests,a sample of one or two cars is used because ________.

A)sampling is more accurate
B)cars are destroyed
C)it is quicker
D)the population is very large

Question 22

The true sampling error is usually not known because ________.

A)µ is unknown
B)µ is a random variable
C)σ² is unknown
D)The sample mean cannot be computed.

Question 23

The mean of all the sample means is ________.

A)
B)µ
C)σ
D)α

Question 24

The size of the sampling error is ________.

A)directly related to the sample size-in other words,the larger the sample size,the larger the sampling error
B)directly related to the population mean-in other words,the larger the mean,the larger the sampling error
C)inversely related to the sample size-in other words,the larger the sample size,the smaller the sampling error
D)inversely related to the population standard deviation-in other words,the smaller the standard deviation,the larger the sampling error

Question 25

The central limit theorem allows us to use a z-statistic to compute probabilities for the sampling distribution of the sample mean.

Question 26

When all the items in a population have an equal chance of being selected for a sample,the process is called ________.

A)simple random sampling
B)z-score
C)sampling error
D)nonprobability sampling

Question 27

As the size of the sample increases,what happens to the shape of the distribution of sample means?

A)It cannot be predicted in advance.
B)It approaches a normal distribution.
C)It is positively skewed.
D)It is negatively skewed.

Question 28

When computing probabilities for the sampling distribution of the sample mean,the z-statistic is computed as z = .

Question 29

To study the population of consumer perceptions of new technology,sampling of the population is preferred over surveying the population because ________.

A)sampling is more accurate
B)we can compute z-scores
C)it is quicker
D)sampling methods are simple

Question 30

What is the difference between a sample mean and the population mean called?

A)Standard error of the mean
B)Sampling error
C)Interval estimate
D)Point estimate

Question 31

Suppose we select every fifth invoice in a file. What type of sampling is this?

A)Random
B)Cluster
C)Stratified
D)Systematic

Question 32

The standard error of the mean is directly related to the sample size.

Question 33

Sampling error is defined as ________.

A) - μ
B)σ
C)σ/n
D)N − n

Question 34

For a given population,the mean of all the sample means ,of sample size n,and the mean of all (N)population observations (X)are ________.

A)equal to
B)not equal
C)equal to - μ
D)equal to the population mean µ

Question 35

All possible samples of size n are selected from a population,and the mean of each sample is determined. What is the mean of the sample means?

A)It is the population mean.
B)It is larger than the population mean.
C)It is smaller than the population mean.
D)It cannot be estimated in advance.

Question 36

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 21 years of age,a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the sample size?

A)4
B)100
C)400
D)1

Question 37

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 21 years of age,a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the number of samples?

A)4
B)100
C)400
D)1

Question 38

For a distribution of sample means constructed by sampling 5 items from a population of 15,________.

A)the sample size is 15
B)there will be 3,003 possible sample means
C)the mean of the sample means will be 3
D)the standard error will be 1

Question 39

The standard error of the mean measures the dispersion of the sampling distribution of the sample mean.

Question 40

When dividing a population into subgroups so that a random sample from each subgroup can be collected,what type of sampling is used?

A)Simple random sampling
B)Systematic sampling
C)Stratified random sampling
D)Cluster sampling

Question 41

Bones Brothers & Associates prepare individual tax returns. Over prior years,Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes,and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns is between 88 minutes and 92 minutes?

A)Approximately 1
B)0.1664
C)0.8336
D)0.8472

Question 42

Bones Brothers & Associates prepare individual tax returns. Over prior years,Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes,and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the standard error of the mean?

A)14 minutes
B)140 minutes
C)1.4 minutes
D)90 minutes

Question 43

The mean of all possible sample means is equal to ________.

A)the population variance
B)σ /
C)the sample variance
D)the population mean

Question 44

According to the central limit theorem,________.

A)the population mean and the mean of all sample means are equal
B)increasing sample size decreases the dispersion of the sampling distribution
C)the sampling distribution of the sample means is approximately normally distributed
D)the sampling distribution of the sample means will be skewed

Question 45

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million,and so on. Samples were then selected from each of these groups. What is this type of sampling called?

A)Simple random sampling
B)Stratified random sampling
C)Cluster sampling
D)Systematic sampling

Question 46

Bones Brothers & Associates prepare individual tax returns. Over prior years,Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the mean time to complete a tax form?

A)The population distribution is skewed to the right.
B)The population distribution is skewed to the left.
C)The population distribution is normal.
D)The shape of the population distribution does not matter.

Question 47

Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20. The population standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21?

A)0.4772
B)0.0228
C)0.9544
D)1.0000

Question 48

An experiment involves selecting a random sample of 256 middle managers for study. One item of interest is their annual income. The sample mean is computed to be $35,420. If the population standard deviation is $2,050,what is the standard error of the mean?

A)$128.125
B)$138.36
C)$2,050
D)$8.01

Question 49

Bones Brothers & Associates prepare individual tax returns. Over prior years,Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes,and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns for this year is greater than 92?

A)Approximately 0
B)0.0832
C)0.4168
D)0.0764

Question 50

A statewide sample survey is to be conducted. First,the state is subdivided into counties. Seven counties are selected at random,and further sampling is concentrated on these seven counties. What type of sampling is this?

A)Simple random
B)Systematic random sampling
C)Cluster sampling
D)Stratified sampling

Question 51

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations,the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation of 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

A)0.3782
B)0.0222
C)1.0
D)0.5

Question 52

The weight of trucks traveling on a particular section of I-475 has a population mean of 15.8 tons and a population standard deviation of 4.2 tons. What is the probability a state highway inspector could select a sample of 49 trucks and find the sample mean to be 14.3 tons or less?

A)0.0062
B)0.3632
C)0.1368
D)0.4938

Question 53

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is between 19 hours and 20 hours?

A)2.00
B)0.4772
C)−2.00
D)Cannot be calculated based on the given information.

Question 54

Sampling error is the difference between a sample statistic and its corresponding ________.

A)sample mean
B)variance
C)population parameter
D)trend

Question 55

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is less than 19.25 hours?

A)0.4332
B)0.8664
C)0.0668
D)0.0181

Question 56

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the standard error of the mean?

A)0.50
B)6.00
C)0.25
D)2.00

Question 57

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The sample mean tread wear was 50,000 miles,with a population standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?

A)50,000
B)3,500
C)500
D)35

Question 58

Which of the following is the standard error of the mean?

A)σ
B)x/n
C)σ /
D)s

Question 59

For a population that is not normally distributed,the distribution of the sample means will ________.

A)be negatively skewed
B)approach a normal distribution
C)be positively skewed
D)take the same shape as the population

Question 60

According to the central limit theorem,________.

A)sample size is important when the population is not normally distributed
B)increasing the sample size decreases the dispersion of the sampling distribution
C)the sampling distribution of the sample means is uniform
D)the sampling distribution of the sample means will be skewed

Question 61

For a given population with a normal probability distribution,the sampling distribution of is a normal probability distribution for ________.

A)small sample sizes only
B)any sample size
C)large sample sizes only
D)sample sizes greater than 30 only

Question 62

How many different samples of size 4 can be selected from a population of size 8?

A)8
B)32
C)70
D)1680

Question 63

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,000 miles and a population standard deviation of 4,000 miles. Suppose you bought a set of four tires; what is the likelihood the mean tire life of these four tires is more than 66,000 miles?

A)0.0013
B)0.9987
C)0.4987
D)0.9544

Question 64

The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find the mean of this sample is between 95 and 105?

A)0.0182
B)0.9818
C)1.00
D)Very unlikely

Question 65

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,000 miles and a population standard deviation of 4,000 miles. Suppose we select a sample of 40 tires and use a simulator to determine the tread life. What is the likelihood of finding that the sample mean is between 59,050 and 60,950?

A)0.4332
B)0.8664
C)1.00
D)Very likely

Question 66

The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find the mean of this sample is less than 95?

A)0.0091
B)0.9818
C)0.4909
D)0.9544

Question 67

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

A)0.9544
B)0.0160
C)0.0986
D)0.9104

Question 68

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,000 miles and a population standard deviation of 4,000 miles. Suppose we select a sample of 40 tires and use a simulator to determine the tread life. What is the standard error of the mean?

A)632.46
B)40
C)4,000
D)Cannot be determined.

Question 69

The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103?

A)0.3264
B)0.9428
C)0.4702
D)0.7471

Question 70

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,000 miles and a population standard deviation of 4,000 miles. Suppose you bought a set of four tires,what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles?

A)0.4332
B)0.8664
C)1.00
D)Very likely

Question 71

The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample exceeds 104?

A)0.0294
B)0.9412
C)Approximately 1
D)0.9706