Deck 7: Sampling and Sampling Distributions

Question 1

The sampling distribution of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

Answer 1

True

Question 2

The central limit theorem states that as sample size increases,the population distribution more closely approximates a normal distribution.

Answer 2

False

Question 3

A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.

Answer 3

True

Question 4

If a population is known to be normally distributed,then it follows that the sample standard deviation must equal $\sigma$ .

Question 5

If the sampled population distribution is skewed,then in most cases the sampling distribution of the mean can be approximated by the normal distribution if the sample size n is at least 30.

Question 6

The standard deviation of all possible sample proportions increases as the sample size increases.

Question 7

If we have a sample size of 100 and the estimate of the population proportion is .10,we can estimate the sampling distribution of with a normal distribution.

Question 8

If the sampled population is exactly normal distribution,then the sampling distribution of is also expected to be normal regardless of the sample size.

Question 9

A sample size of 500 is sufficiently large enough to conclude that the sampling distribution of is a normal distribution,when the estimate of the population proportion is .995.

Question 10

The sampling distribution of must be a normal distribution with a mean 0 and standard deviation 1.

Question 11

If a population is known to be normally distributed,then it follows that the sample mean must equal the population mean.

Question 12

A minimum variance,unbiased point estimate has a variance that is as small or smaller than the variances of any other unbiased point estimate.

Question 13

The standard deviation of the sampling distribution of the sample mean is $\sigma$ .

Question 14

For any sampled population,the population of all sample means is approximately normally distributed.

Question 15

As the sample size increases,the standard deviation of the sampling distribution increases.

Question 16

In order to select a stratified random sample,we divide the population into overlapping groups of similar elements.

Question 17

If p = .8 and n = 50,then we can conclude that the sampling distribution of is approximately a normal distribution.

Question 18

If p = .9 and n = 40,then we can conclude that the sampling distribution of is approximately a normal distribution.

Question 19

We can randomly select a sample from an infinite population of potential process measurements by sampling the process at different and equally spaced time points.

Question 20

The reason sample variance has a divisor of n-1 rather than n is that it makes the variance an unbiased estimate of the population variance.

Question 21

The central limit theorem states that as the sample size increases the distribution of the sample ________ approach the normal distribution.

A)medians
B)means
C)standard deviations
D)variances

Question 22

A manufacturing company measures the weight of boxes before shipping them to the customers.If the box weights have a population mean and standard deviation of 90 lbs.and 24 lbs.respectively,then based on a sample size of 36 boxes,the probability that the average weight of the boxes will exceed 94 lbs.is:

A)34.13%
B)84.13%
C)15.87%
D)56.36%
E)16.87%

Question 23

If we have a sample size of 100 and the estimate of the population proportion is .10,the mean of the sampling distribution of the sample proportion is:

A)0.0009
B)0.10
C)0.03
D)0.90
E)0.09

Question 24

The mean of the sampling distribution of is always equal to the mean of the sampled population.

Question 25

_____________ is the difference between a numerical description of the population and the corresponding descriptor of the sample.

A)Sampling error
B)Non-observation error
C)Observation error
D)Non-response

Question 26

A 'Yes or No' question is _____________.

A)Dichotomous
B)Multiple Choice
C)Open-ended
D)Systematic

Question 27

The population of all sample proportions has a normal distribution if the sample size (n)is sufficiently large.The rule of thumb for ensuring that n is sufficiently large is:

A)np $\ge$ 5
B)n(1 - p)5
C)np $\le$ 5
D)n(1 - p) $\le$ .5 and np $\le$ 5
E)np .5 and n(1 - p) $\ge$ 5

Question 28

If the sampled population has a mean 48 and standard deviation 16,then the mean and the standard deviation for the sampling distribution of for n = 16 are:

A)4 and 1
B)12 and 4
C)48 and 4
D)48 and 1
E)48 and 16

Question 29

Consider a sampling distribution formed based on n = 3.The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements $\sigma$ .

A)Always
B)Sometimes
C)Never

Question 30

If the sample size n is infinitely large,then is an unbiased estimator of. .

Question 31

A manufacturing company measures the weight of boxes before shipping them to the customers.If the box weights have a population mean and standard deviation of 90 lbs.and 24 lbs.respectively,then based on a sample size of 36 boxes,the probability that the average weight of the boxes will be less than 84 lbs.is:

A)16.87%
B)93.32%
C)43.32%
D)6.678%
E)84.13%

Question 32

_____________ occurs when some population elements are excluded from the process of selecting the sample.

A)Non-response
B)Error of observation
C)Undercoverage
D)Sampling error

Question 33

If a population distribution is known to be normal,then it follows that:

A)The sample mean must equal the population mean.
B)The sample mean must equal the population mean for large samples.
C)The sample standard deviation must equal the population standard deviation.
D)All of the above.
E)None of the above.

Question 34

Whenever the population has a normal distribution,the sampling distribution of is normal or near normal distribution:

A)For only large sample sizes
B)For only small sample sizes
C)For any sample size
D)For only samples of size 30 or more

Question 35

The sample standard deviation s is an unbiased estimator of the population standard deviation .

Question 36

As the sample size ______________ the variation of the sampling distribution of ___________.

A)Decreases,decreases
B)Increases,remains the same
C)Decreases remains the same
D)Increases,decreases
E)None of the above

Question 37

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

Question 38

A common practice in selecting a sample from a large geographic area is multi-stage cluster sampling.

Question 39

If we have a sample size of 100 and the estimate of the population proportion is .10,the standard deviation of the sampling distribution of the sample proportion is:

A).0009
B).03
C)3
D)9
E).10

Question 40

A low response rate has no effect on the validity of a survey's findings.

Question 41

The sampling distribution of the sample mean is a normal distribution for ________ sample sizes regardless of the shape of the corresponding population distribution.

A)Random
B)Large
C)Larger than 50
D)Small

Question 42

The spread of the sampling distribution of is ____________ the spread of the corresponding population distribution sampling distribution.

A)Larger than
B)Smaller than
C)The same as
D)Exactly ½

Question 43

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue.The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What is the probability that at least 30 accounts will be classified as delinquent?

A)31.86 %
B)18.14 %
C)81.86 %
D)63.72 %
E)75.84 %

Question 44

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at least 3.16 inches?

A)97.72 %
B)5.48 %
C)94.52 %
D)44.52 %
E)2.28 %

Question 45

For non-normal populations,as the sample size (n)___________________,the distribution of sample means approaches a(n)________________ distribution.

A)Decreases,Uniform
B)Increases,Normal
C)Decreases,Normal
D)Increases,Uniform
E)Increases,Exponential

Question 46

According to a hospital administrator,historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted. Sixty-four (64)patients indicated that they were dissatisfied with the after surgery care.What are the mean and the standard deviation of the sampling distribution of ?

A)16% and .034%
B)20% and 1.83%
C)20% and 2%
D)20% and .034%
E)20% and 16%

Question 47

If a sample size is at least _____,then for any sampled population,we can conclude that the sample means are approximately normal.

A)25
B)20
C)30
D)50

Question 48

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at most 3.1 inches?

A)84.13%
B)100 %
C)71.57 %
D)28.43 %
E)15.87 %

Question 49

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue.The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What are the mean and the standard deviation of the sampling distribution of ?

A)14 and 250
B).14 and .1204
C)35 and 5.486
D).14 and .0219
E)35 and 30.1

Question 50

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue.The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What is the probability that no more than 40 accounts will be classified as delinquent?

A)42.07 %
B)92.07 %
C)7.93 %
D)40.15 %
E)90.15%

Question 51

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)Cluster sampling
B)Sampling error
C)Sampling distribution of the mean
D)Central Limit Theorem

Question 52

_____ says that if the sample size is sufficiently large,then the sample means are approximately normally distributed.

A)Cluster sampling
B)Sampling error
C)Sampling distribution of the mean
D)Central Limit Theorem

Question 53

According to a hospital administrator,historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted. What is the probability that at least 70 patients will not be satisfied with the after-surgery care?

A)89.44%
B)39.44%
C)10.56%
D)78.88%
E)84.49%

Question 54

For large samples,the sampling distribution of is approximately normal with a mean of _____.

A)
B)
C)
D)Z

Question 55

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the standard deviation of the sampling distribution of the sample mean?

A).03
B).01
C).1732
D).0577
E).10

Question 56

The mean of the sampling distribution of the sample proportion is equal to _____ when the sample size is sufficiently large.

A) $\mu$
B)p
C)p * n
D)(1-p)

Question 57

The notation for the standard deviation of the sampling distribution of the sample mean is __________.

A)
B) $\sigma$ ^x
C)
D)

Question 58

According to a hospital administrator,historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted. What is the probability that less than 64 patients will not be satisfied with the after-surgery care?

A)47.72%
B)2.28%
C)97.72%
D)95.44%
E)4.56%

Question 59

If the sampled population is finite and at least _____ times larger than the sample size,the standard deviation of decreases as the sample size increases.

A)5
B)20
C)30
D)10

Question 60

If we wish to estimate a population parameter by using a sample statistic,we are using _____.

A)Cluster sampling
B)Point estimation
C)Random sampling
D)Response bias

Question 61

The ___________ is a minimum-variance unbiased point estimate of the mean of a normally distributed population.

A)Sample mean
B)Sample variance
C)Sample standard deviation
D)Observed mean

Question 62

As the sample size ___________,the standard deviation of the population of all sample proportions increases.

A)Increases
B)Stays the same
C)Is variable
D)Decreases

Question 63

The population of lengths of aluminum - coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.3 inches.What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 inches long?

A).8413
B).6293
C).3707
D).1587

Question 64

Suppose that 60 percent of the voters in a particular region support a candidate.Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.

A).0155
B).9952
C).9484
D).9902

Question 65

The number of defectives in the samples of 50 observations each is the following: 5,1,1,2,3,3,1,4,2,3.What is the estimate of the population proportion of defectives?

A).25
B).50
C).05
D).42

Question 66

Find

A)0.20
B)200
C)20
D)2.00

Question 67

The number of defectives in the samples of 100 observations each is the following: 1,2,1,0,2,3,1,4,2,1.What is the estimate of the population proportion of defectives?

A).017
B).17
C).016
D).16

Question 68

Find

A).8413
B).4602
C).5398
D).1587

Question 69

Find

A).0764
B).9998
C).9236
D).0001

Question 70

Find

A).1587
B).8413
C).6293
D).3707

Question 71

Find

A)1.000
B)2.25
C).9878
D).0122

Question 72

The _______________________ of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

A)Sample mean
B)Sampling distribution
C)Probability
D)Observations

Question 73

The population of all _________________ proportions is described by sampling distribution of .

A)Population
B)Random
C)Observed
D)Sample

Question 74

Packages of sugar bags for Sweeter Sugar Inc.have an average weight of 16 ounces and a standard deviation of 0.2 ounces.The weights of the sugar bags are normally distributed.What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?

A).0500
B).3520
C).9332
D).0668

Question 75

A PGA (Professional Golf Association)tournament organizer is attempting to determine whether hole (pin)placement has a significant impact on the average number of strokes for the 13^th hole on a given golf course.Historically,the pin has been placed in the front right corner of the green,and the historical mean number of strokes for the hole has been 4.25,with a standard deviation of 1.6 strokes.On a particular day during the most recent golf tournament,the organizer placed the hole (pin)in the back left corner of the green.64 golfers played the hole with the new placement on that day.Determine the probability of the sample average number of strokes exceeding 4.75.

A).9938
B).4013
C).0062
D).3783

Question 76

An unbiased estimate of is _____.

A)s
B)
C)
D) $\sigma$

Question 77

Find

A).9944
B).4483
C).5517
D).1056

Question 78

Suppose that 60 percent of the voters in a particular region support a candidate.Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.

A).9015
B).8030
C).0155
D).7939

Question 79

As the sample size increases the variability of the sampling distribution of the mean ______________.

A)Increases
B)Stays the same
C)Is variable
D)Decreases

Question 80

Find

A).9786
B).9999
C).0214
D).9893