Deck 8: Sampling Methods and the Central Limit Theorem

Question 1

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

Answer 1

True

Question 2

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 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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 6

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

Question 7

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 8

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

Question 9

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

Question 10

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

Question 11

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 $\sigma$ ² and the variance equal to $\sigma$ ^2/n.

Question 12

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 13

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

Question 14

Based on the central limit theorem, sampling error will decrease as sample size increases.

Question 15

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 16

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

Question 17

When deciding to take a sample from a population, the amount of time required to take the sample is not important.

Question 18

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 19

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 20

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

Question 21

The true sampling error is usually not known because

A) µ is unknown
B) µ is a random variable
C) $\sigma$ 2 is unknown
D) The sample mean cannot be computed

Question 22

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

Question 23

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women, 18-21 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.

A) The sample size was 4.
B) The sample size was 100.
C) The sample size was 400.
D) The sample size was 1.

Question 24

The size of the sampling error is

A) Directly related to the sample size, i.e., the larger the sample size, the larger the sampling error.
B) Directly related to the population mean, i.e., the larger the mean, the larger the sampling error.
C) Inversely related to the sample size, i.e., the larger the sample size, the smaller the sampling error.
D) Inversely related to the population standard deviation, i.e., the smaller the standard deviation, the larger the sampling error.

Question 25

When computing probabilities for the sampling distribution of the sample mean, the z-statistic is computed as Z= xbar - mu/sigma

Question 26

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 27

Sampling error is defined as

A) ( - µ)
B) $\sigma$
C) $\sigma$ /n
D) N - n

Question 28

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 3003 possible sample means
C) the mean of the sample means will be 3
D) the standard error will be 1

Question 29

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 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

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

A) Cannot be predicted in advance.
B) Approaches a normal distribution.
C) Positively skewed.
D) Negatively skewed.

Question 32

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

Question 33

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women, 18-21 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.

A) The number of samples was 4.
B) The number of samples was 100.
C) The number of samples was 400.
D) The number of samples was 1.

Question 34

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) The population mean
B) Larger than the population mean
C) Smaller than the population mean
D) Cannot be estimated in advance

Question 35

When testing the safety of cars using crash tests, a sample of 1 or 2 cars is used because

A) Sampling is more accurate.
B) Cars are destroyed.
C) It is quicker.
D) The population is very large.

Question 36

The mean of all the sample means is

A)
B) µ
C) $\sigma$
D) a

Question 37

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

Question 38

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) are equal to ( - x)
D) equal to the population mean, µ

Question 39

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

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

Question 40

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 41

Sampling error is the difference between a corresponding sample statistic and the

A) sample mean.
B) biased sample.
C) population parameter.
D) chance error.

Question 42

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 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 43

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

A) $\sigma$
B) x/n
C)
D) s

Question 44

Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20 and the sample 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) $20

Question 45

A statewide sample survey is to be made. 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
D) Stratified

Question 46

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the standard error of the mean?

A) 0.83
B) 10
C) 0.5
D) 2

Question 47

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 48

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a 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) (50,000/100)
D) (3,500/100)

Question 49

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time is between 1 and 2 hours, i.e., 60 and 120 minutes?

A) Approximately 1
B) 0.1664
C) 0.8336
D) 0.9676

Question 50

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability that a sample mean would exceed 20 hours per week?

A) 1.0
B) 0.5
C) 1.96
D) Cannot be calculated based on the given information.

Question 51

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students study per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability of finding a sample mean less than 18 hours?

A) 0.4820
B) 0.4918
C) 0.0082
D) 0.0181

Question 52

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
B) Stratified random
C) Cluster
D) Systematic

Question 53

According to the central limit theorem,

A) Sample size is important when the population is not normally distributed.
B) Increasing sample size decreases the dispersion of the sampling distribution.
C) The sampling distribution of the sample means Uniform.
D) The sampling distribution of the sample means will be skewed.

Question 54

The mean of all possible sample means is equal to the

A) population variance.
B) .
C) sample variance.
D) population mean.

Question 55

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the standard error of the mean?

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

Question 56

An experiment involves selecting a random sample of 256 middle managers study. One item of interest is their mean annual income. The sample mean is computed to be $35,420 and the sample 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 57

The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 4.2 tons. What is probability that a truck will weigh less than 14.3 tons?

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

Question 58

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. 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 average 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 59

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

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

Question 60

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time will be more than 120 minutes?

A) Approximately zero
B) 0.0832
C) 0.4168
D) 0.0162

Question 61

How many different samples of size 3 can be collected from a population of ten items? ___________

Question 62

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability that average student study time is between 18 and 22 hours?

A) 0.9640
B) 0.0160
C) 0.0360
D) 0.9836

Question 63

Sampling from a population may be preferred because studying all the items in a population may be too ____________.

Question 64

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. Given a class with 9 students, what is the probability that the class' average IQ score is between 85 and 115?

A) 0.4987
B) 3.00
C) 0.0026
D) 0.9974

Question 65

What is the name of the standard deviation of the sampling distribution of the sample means called? ______________________

Question 66

Sampling from a population may be preferred because, contacting or listing the entire population would be too ___________ consuming.

Question 67

A __________________ assumes that each item or person in the population has an equal chance of being included.

Question 68

If the size of a sample equals the size of the population, the sample error is ________.

Question 69

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. You bought four tires. What is the probability that the average mileage of the four tires exceeds 66,000 miles?

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

Question 70

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person would score 130 or more on the test?

A) 0.0228
B) 0.9772
C) 0.4772
D) 0.9544

Question 71

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. For a set of four tires, what is the probability that the average tire life is between 57,000 and 63,000 miles?

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

Question 72

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup? _________

Question 73

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 ______________.

Question 74

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. What is the probability that a tire will last 72,000 miles or more?

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

Question 75

Auditors may select every 20^th file starting with say, the 5^th file in the top drawer. Then file numbers 25, 45, 65, 85, .... are audited. What type of sampling is this? _________________

Question 76

Sometimes, sampling from a population may be preferred because collecting statistics may require that products be __________.

Question 77

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person would score between 85 and 115?

A) 0.3413
B) 0.6826
C) 1.00
D) Very likely

Question 78

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. What is the probability that a tire lasts between 54,000 and 66,000 miles?

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

Question 79

If a population is normally distributed, then the sampling distribution of the sample means will be __________________________.

Question 80

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. You enrolled in a class of 25 students. What is the probability that the class' average IQ exceeds 130?

A) 0.0228
B) 0.9772
C) Approximately zero
D) 0.9544