Deck 7: Statistical Inference: Estimating a Population Mean

Question 1

In order to qualify as a source of random numbers, all of the digits that appear in a random number table must be equally represented and must show no pattern to the way they appear in the table.

Answer 1

True

Question 2

An example of systematic sampling is when every 20th item on a list of population members is selected for inclusion in the sample.

Answer 2

True

Question 3

The sampling distribution of the sample mean is the probability distribution of all possible values of the sample mean when samples of size n are taken from a given population.

Answer 3

True

Question 4

A simple random sample of size n from a population of size N is a sample selected such that each possible sample of size n has a probability of 0.5 of being selected.

Question 5

Destructive testing can be described as a testing procedure that results in the destruction of the item being tested.

Question 6

As sample size n increases the margin of error in an interval estimate of a population mean also increases.

Question 7

In simple random sampling, sampling without replacement is where elements are not replaced once drawn from the population and is the procedure used most often.

Question 8

Sampling with replacement is a sampling procedure in which a population member could be included more than once in the sample.

Question 9

In statistical inference, data from the sample is used to estimate the population parameter.

Question 10

The sampling distribution of the sample mean is the probability distribution of all possible values of the sample mean when samples of size n-1 are taken from a given population.

Question 11

A finite population correction (fpc) factor increases the size of the standard error of the mean when sampling is done without replacement from a finite population.

Question 12

The central limit theorem states that as sample size increases, the sampling distribution of the sample mean rapidly approaches the bell shape of a normal distribution, regardless of the shape of the parent population.

Question 13

Simple random sampling is a sampling method which ensures that every combination of n members of the population has an equal chance of being selected.

Question 14

The finite population correction factor (fpc) is required in the formula for the standard error whenever n/N < .10.

Question 15

In simple random sampling, every combination of n members of the population has an equal chance of being selected.

Question 16

The law of large numbers establishes that sample means will approach the mean of the parent population as sample size increases.

Question 17

Sampling without replacement is a sampling procedure in which a population member could be included more than once in the sample.

Question 18

Stratified sampling works best when differences between groups (strata) are small and differences within groups are large.

Question 19

A random sample is a sample selected according to the laws of chance and in a way that gives every member of the population a measurable, non-zero probability of being included.

Question 20

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

Question 21

Which of the following is not a proper method for selecting a random sample?

A)stratified sampling
B)judgment sampling
C)systematic sampling
D)cluster sampling
E)none of the above; all are proper methods

Question 22

The degrees of freedom in the t distribution represents the number of "independent" terms involved in the sample standard deviation calculation.

Question 23

The margin of error is the minimum difference we would expect between a particular sample mean and the overall population mean at a specified level of confidence.

Question 24

To determine the proportion of students on campus who would be interested in having coin operated snack machines installed in the Bellarmine dormitory basement, I send out a simple yes or no poll to all Bellarmine dormitory residents.What sampling method am I using?

A)simple random sampling
B)stratified random sampling
C)judgment sampling
D)systematic random sampling
E)cluster random sampling

Question 25

Using the cluster random sampling method would be most useful when:

A)surveying who wants to order pizza for lunch in Mr.Green's second period class.
B)surveying to determine the percentage of swimmers on the college team who are likely to return next season.
C)surveying to determine the academic performance of California high school students
D)surveying to measure the job satisfaction or employees of a small business.
E)surveying to determine the average salaries of people in a group of zipcodes.

Question 26

A single number that is the best guess of a population parameter based on sample results is called:

A)a sample statistic
B)a point estimate
C)an interval estimate
D)a probability distribution
E)a sample parameter

Question 27

A simple random sample of size n from a 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
E)none of the above

Question 28

Using a nonrandom sample to estimate the mean of a population:

A)should never be done
B)will result in a smaller sampling error than a random sample
C)requires the help of a random number table
D)means that possible error cannot be systematically measured
E)none of the above

Question 29

A sample selected according to the laws of chance so that every member of the population will have a measurable, non-zero probability of being included in the sample is called a:

A)judgment sample
B)random sample
C)simple sample
D)population sample
E)systematic sample

Question 30

The method of sampling that ensures that every subgroup of interest in a particular study is represented in the sample is called:

A)systematic random sampling
B)stratified random sampling
C)grouped random sampling
D)randomized group sampling
E)cluster random sampling

Question 31

The purpose of statistical inference is to provide information about the:

A)sample based on information contained in the population
B)population based on information contained in the sample
C)population based on information contained in the population
D)mean of the sample based on the mean of the population
E)none of the above

Question 32

The standard error is the amount added to and subtracted from the sample mean to obtain an interval estimate of the population mean.

Question 33

Some of the reasons for sampling rather than doing a full census (100% inspection) of an entire population include:

A)lowering costs
B)the opportunity to look more carefully at fewer items
C)saving time
D)reducing the consequences of destructive testing
E)all of the above

Question 34

The margin of error is the maximum difference we would expect between a particular sample mean and the overall population mean at a specified level of confidence.

Question 35

Statistical inference is:

A)not the same as inferential statistics.
B)drawing conclusions from a data set describing an entire population.
C)reaching conclusions about characteristics of an entire population by using probability distributions.
D)reaching conclusions about characteristics of an entire population using data from a subset of that population.
E)reaching conclusions about characteristics of a sample using data from the population.

Question 36

An examination of all the members of a particular population is called a(n):

A)infinite population
B)finite population
C)cluster sampling
D)census
E)simple random sample

Question 37

You produce a confidence interval estimate of a population mean from a simple random sample of size n.If sample size is doubled and the confidence requirement remains the same, the width of the new interval estimate will be half the width of the original.

Question 38

Fifteen freshmen, 15 sophomores, 15 juniors, and 15 seniors of a university were surveyed to study the sleeping habits of college students throughout their college years.The best description of the sampling method used is

A)systematic random sampling
B)stratified random sampling
C)judgment sampling
D)simple random sampling
E)cluster random sampling

Question 39

A non-random sampling procedure that involves deliberately, rather than randomly, selecting certain "representative" population members for inclusion in the sample is called:

A)judgment sampling
B)central limit sampling
C)exhaustive sampling
D)stratified sampling
E)cluster sampling

Question 40

An 80% confidence interval will be twice as wide as a 40% confidence interval.

Question 41

The sampling distribution of the sample mean:

A)is the probability distribution showing all possible values of the sample mean
B)is used as a point estimate of the population mean $\mu$
C)is an unbiased estimator
D)shows the distribution of all possible values of $\mu$
E)none of the above

Question 42

When constructing a confidence interval, an increase in sample size will:

A)increase the margin of error and increase the standard error
B)increase the margin of error and decrease the standard error
C)decrease both the margin of error and the standard error
D)increase both the margin of error and the standard error
E)will have no effect on the confidence interval

Question 43

The statistical principle that guarantees a near-normal sampling distribution of the sample mean no matter what the shape of the parent population distribution is:

A)law of large numbers
B)central limit theorem
C)normal principle
D)sampling theory
E)probability

Question 44

Which of the following is a key property of the sampling distribution of the sample mean?

A)for large enough samples the shape of the sampling distribution will be approximately normal
B)the sampling distribution is centered on the mean of the population
C)the standard deviation of the sampling distribution can be computed as the population standard deviation divided by the square root of the sample size
D)all of the above
E)none of the above

Question 45

Before any order is shipped, inspectors at Alvarez Manufacturing test a sample of finished units for breaking strength.You select a simple random sample of units from a recently completed order and find that the sample average breaking strength is 814 pounds.From the sample selected, you construct a 95% confidence interval estimate of the average breaking strength you could expect to find if all the units in the order were tested.The interval turns out to be 814 ± 7.5 lbs.How would you interpret your result?

A)Approximately 95% of the units in the order will have a breaking strength of between 806.5 lbs.and 821.5 lbs.
B)Approximately 95% of the units in the sample have a breaking strength of between 806.5 lbs.and 821.5 lbs.
C)Approximately 95% of the units in the population will have a breaking strength of between 806.5 and 821.5 lbs.
D)We can be 95% confident that all the units in the order have a breaking strength of between 806.5 lbs.and 821.5 lbs.
E)If we were to repeat this estimating procedure a large number of times, approximately 95% of the intervals we construct would contain the actual order average breaking strength.

Question 46

What is the margin of error?

A)the standard error times the appropriate Z score
B)the standard error divided by the appropriate Z score
C)the appropriate Z score divided by the standard error
D)the standard error plus the appropriate Z score
E)the standard deviation times the appropriate Z score

Question 47

Which of the following is the amount that is added to or subtracted from the sample mean to construct an interval estimate of the population mean?

A)level of significance
B)margin of error
C)standard error
D)z score
E)confidence coefficient

Question 48

Which of the following is NOT a factor influencing the width of a confidence interval?

A)the confidence level
B)the sample size n
C)the variation in the population as measured by $\sigma$
D)the size of the sample mean
E)none of the above; all are factors

Question 49

Which of the following statements is TRUE about the Central Limit Theorem?

A)As the sample size decreases, the sampling distribution of the sample mean approaches the bell shape of a normal distribution.
B)As the sample size increases, the sampling distribution of the sample mean approaches the bell shape of a normal distribution.
C)As the sample size decreases, the sampling distribution of the sample mean approaches the flat shape of a uniform distribution.
D)As the sample size increases, the sampling distribution of the sample mean approaches the flat shape of a uniform distribution.
E)As the sample size increases, the sampling distribution of the sample mean approaches the skewed positive shape of the t distribution.

Question 50

The sampling error is the:

A)same as the standard error of the mean
B)error caused by selecting a bad sample
C)standard deviation multiplied by the sample size
D)difference between the value of the sample mean and the value of the population mean
E)none of the above

Question 51

What is the purpose of the sampling distribution of the sample mean?

A)to obtain the mean of a sample set of data
B)to construct a probability distribution based on a list of numbers
C)to provide a link between sample results and population parameters
D)to describe the distribution of a variable in the entire population
E)to build a confidence interval

Question 52

Which of the following is NOT a property of the sampling distribution of the sample mean?

A)approximately normal shape for large sample sizes
B)a mean equal to the population mean
C)a standard deviation influenced by sample size and variation
D)a center equal to the mean of a randomly selected sample
E)none of the above; all are a property

Question 53

Which of the following describes how an interval estimate is constructed?

A)set the level of significance and then calculate the z-score
B)point estimate plus and minus the standard error
C)point estimate plus and minus the margin of error
D)point estimate plus and minus the z score
E)set the confidence coefficient and then calculate the z-score

Question 54

Which of the following is a factor that influences interval width?

A)confidence level
B)sample size n
C)variation in the population as measured by $\sigma$
D)all of the above
E)none of the above

Question 55

Which of the following best describes the sampling distribution of the sample mean?

A)It is the probability distribution of all possible values of the sample mean when samples of size n are taken from a given population.
B)For small sample sizes, the shape will be approximately normal
C)The sampling distribution is centered on the standard deviation
D)The mean determines the spread or width of the distribution
E)All of the above

Question 56

The fact that the sampling distribution of the sample mean can be approximated by a normal distribution whenever the sample size is large is based on the:

A)assumption that the population has a normal distribution
B)fact that there are tables of areas for the normal distribution
C)central limit theorem
D)all of the above
E)none of the above

Question 57

Which of the following is NOT a factor influencing the width of a confidence interval?

A)the population mean
B)the population standard deviation
C)the sample size
D)the confidence level
E)all of the above

Question 58

The difference between the mean of any given sample and the mean of the population is called the:

A)margin of error
B)prediction error
C)sampling error
D)standard error
E)error of estimate

Question 59

According to the central limit theorem, as the sample size becomes larger the sampling distribution of the sample mean approaches a:

A)binomial distribution
B)Poisson distribution
C)hypergeometric distribution
D)normal distribution
E)none of the above

Question 60

Which of the following is NOT a property of the sampling distribution of the sample mean?

A)For large enough sample sizes, the shape of the distribution is approximately normal.
B)The distribution is centered on the mean of the population.
C)The standard deviation of the distribution can be computed as the sample standard deviation divided by the square root of the population size.
D)The distribution links sample results to population characteristics.
E)None of the above; all are properties.

Question 61

A population consists of items A, B, C, and D.A simple random sample will be selected from this population.Choose from the alternatives below the list all the possible samples of size 2.

A)AB, AD, AC, BC, BB, CD
B)AC, AD, AB, BA, BC, CD
C)AB, AC, AD, BC, BD, CD
D)AB, AC, AD, BA, BD, CD
E)AD, AC, BA, DB, DC, AB

Question 62

One of the factors that plays a significant role in determining the sample size needed to achieve a desired margin of error is the:

A)degree of variation in the population of values.
B)population mean.
C)sample mean.
D)degrees of freedom of the t-distribution.
E)all of the above.

Question 63

From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected.For an interval estimation of the population mean, the proper distribution to use is the:

A)t distribution with 24 degrees of freedom
B)t distribution with 26 degrees of freedom
C)normal distribution
D)standard normal distribution
E)none of the above

Question 64

Which of the following factors would be used to determine sample size?

A)confidence level
B)the required precision (margin of error)
C)the degree of variation in the population as measured by $\sigma$
D)all of the above
E)none of the above

Question 65

You plan to select a simple random sample to estimate a population average.You initially decide to construct a confidence interval that is no wider than plus or minus 5.0.Making a rough estimate of the variability in the population, you determine the required sample size.Choose which of the four situations described below would require you to increase your sample size.Assume any factor not mentioned remains constant.There may be more than one answer.

A)You want a higher level of confidence.
B)You want a tighter interval.
C)You decide that you can live with a lower confidence level.There is more variability in the population of values than you had first estimated.
D)You want a tighter interval.You require a higher level of confidence.There is less variability in the population of values than you had first estimated.
E)Both a and b are correct.

Question 66

Which of the following is NOT true of the t distribution?

A)The mean of the t distribution is zero.
B)A specific t distribution depends on the parameter known as the degrees of freedom.
C)A t distribution with more degrees of freedom has more dispersion.
D)As the number of the degrees of freedom increases, the difference between the t distribution and the standard normal distribution becomes smaller .
E)None of the above, all are characteristics.

Question 67

Suppose you plan to build a 98% confidence interval estimate of a population mean, using a sample of size 121.You will be estimating the population standard deviation with the sample standard deviation.The appropriate t-value for your interval would be ____ which you could approximate with a z score of _______ from the normal table.

A)2.358, 2.33
B)1.289, 2.33
C)1.658, 1.96
D)1.980, 1.96
E)2.617, 2.33

Question 68

From a population that is normally distributed with an unknown standard deviation, a sample of size 20 elements is selected.To construct an interval estimate of the population mean, the proper distribution to use is the:

A)t distribution with 19 degrees of freedom
B)t distribution with 21 degrees of freedom
C)z distribution
D)standard normal distribution
E)none of the above

Question 69

The __________ in an interval estimate of μ measures the maximum difference we would expect between the sample mean and the population mean at a given level of confidence.

A)degrees of freedom
B)finite population correction factor
C)margin of error
D)standard error
E)sampling error

Question 70

In the sampling distribution of the sample mean, approximately 95.5% of the sample means will be within_______ standard error(s) of the population mean.

A)1.00
B)1.96
C)2.00
D)2.58
E)3.00

Question 71

Which of the following is a NOT a property of the t distribution?

A)For degrees of freedom less than 5, the normal distribution closely approximates the t distribution.
B)It has a center of 0.
C)It tends to be wider and flatter than the normal distribution.
D)all of the above
E)none of the above; they are all t distribution properties.

Question 72

Suppose you plan to build a 90% confidence interval estimate of a population mean, using a sample of size 3.You will be estimating the population standard deviation with the sample standard deviation.Assuming the population distribution is approximately normal, the appropriate t value for your interval would be _____ .If you had used a z score instead of the t value here, the z score for the 90% interval would be much too small.In fact the z score for a 90% interval is only ______ .

A)4.303, 1.65
B)6.965, 1.96
C)2.920, 1.65
D)1.886, 1.65
E)2.353, 1.96

Question 73

Intervals constructed using a __________ to collect a given percentage of values will be wider than comparable intervals constructed using a __________.

A)t distribution; normal distribution
B)normal distribution; parent population
C)parent population; normal distribution
D)normal distribution; t distribution
E)population distribution, sample distribution

Question 74

__________ is a sampling method that ensures that every combination of n members of a population has an equal chance of being selected.

A)unrestricted random sampling
B)systematic random sampling
C)cluster random sampling
D)judgment sampling
E)stratified sampling

Question 75

You want to estimate the average GMAT score for all students who took the Logitano GMAT Preparation course during the past 2 years.You select a random sample of 100 such students from a comprehensive list of all students who took the course over the last two years and find that the average GMAT score for the sample was 1040.Suppose now you build a 95% confidence interval estimate of the average score for the population of Logitano students represented here and the interval turns out to be 1040 ± 10 points.How would you interpret your result?

A)We can be 95% confident that the interval 1030 to 1050 contains the average score for the entire population of Logitano students.
B)The score for 95% of all Logitano students will be between 1030 and 1050.
C)There is a 5% chance that not all Logitano students scored between 1030 and 1050.
D)We can be 95% confident that all of Logitano students scored between 1030 and 1050.
E)Ninety-five percent of the scores for all Logitano students will be between 1030 and 1050.

Question 76

Torres Electronics wants to estimate the average years of seniority for employees working for the company.The files of 49 workers are selected at random.Average seniority for those in the sample is 13.6 years.Assume you know the population standard deviation is 5.2 years.You proceed to construct a 95% confidence interval estimate of average seniority for the full population of company employees.Which, if any, of the following factors would cause you to change the upper and lower bounds by more than 1/10 of a year for the interval you would produce in the situation described above? (Consider each factor independent of the others.)

A)The standard deviation of the seniority distribution for the population of company employees is unknown, but the sample standard deviation is 5.2 years.
B)The shape of the seniority distribution for the population of company employees is decidedly not NORMAL.The population size is 10,000.
C)The size of the company employee population is known to be 5000.
D)The size of the company employee population is known to be 100.
E)None of the factors would cause a change larger than 1/10 of a year.

Question 77

A random sample of 40 online retailers is selected to estimate the average price of a particular item.The average price in the sample is $1.38.Suppose you build a 99% confidence interval estimate of the average price of the item for the population of online retailers represented here.Suppose further that the interval turns out to be $1.38 ± $.20.How would you interpret your result?

A)The price of the item for 99% of all online retailers who sell the item will be between $1.18 and $1.58.
B)The price of the item for 99% of the online retailers in the sample is between $1.18 and $1.58.
C)We can be 99% confident that all online retailers who sell the item charge between $1.18 and $1.58 for the item.
D)We can be 99% confident that the interval $1.29 to $1.47 contains the average price of the item for the population of online retailers who sell the item.
E)We can be 99% confident that the interval $1.29 to $1.47 contains the average price of the item for the sample of online retailers we sampled.

Question 78

The normal approximation to the t distribution is commonly used:

A)when the sample size is large, greater than 30
B)only when the sample size is large, greater than 100
C)it would never be used
D)only when the central limit could apply
E)none of the above

Question 79

A population consists of items A, B, C, and D.A simple random sample will be selected from this population.Choose from the alternatives below the list of all the possible samples of size 3.

A)ACB, ABD, ACD, BCD
B)ABC, ABD, ACB, BCD
C)ABC, CAD, ACD, BCD
D)ABC, ABD, ADB, BCD
E)ACB, ABD, DBA, CDB

Question 80

You take all possible samples of size 100 from a very large population of values.The mean of the population is 550.The standard deviation is 50.You compute the mean of each sample.95% of the sample means will be greater than _________.

A)558.2
B)541.8
C)560.0
D)545.4
E)555.3