Deck 6: Sampling Distributions

Question 1

As the sample size increases,the mean of the sampling distribution of $\bar { x }$
decreases.

Answer 1

False

Question 2

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.

Answer 2

True

Question 3

The sampling distribution of the sample mean $\bar { x }$ is the probability distribution of the population of all possible values of the sample mean that could be obtained from all possible samples of the same sample size.

Answer 3

True

Question 4

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

Question 5

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

Question 6

The sampling distribution of a sample proportion is approximately normal if and only if np

Question 7

If the sampled population has a normal distribution,then the sampling distribution of $\bar { x }$ is also normal regardless of the sample size.

Question 8

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

Question 9

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.

Question 10

If we take a sample of any size from a population with mean $\mu$
and standard deviation $\sigma$ ,then the standard deviation of the sampling distribution of the sample mean $\bar { x }$ is $\sigma$ .

Question 11

Like the Empirical Rule,the Central Limit Theorem is only applicable to symmetric distributions.

Question 12

If we have a sample size of 100 and a population proportion of 0.10,we can approximate the sampling distribution of $\hat { p }$ with a normal distribution.

Question 13

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

Question 14

The sample mean is always equal to the population mean whenever the sample mean is computed from 30 or more observations.

Question 15

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

Question 16

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

Question 17

If a population is known to be normally distributed,then it follows that the sample mean $\bar { x }$ must equal the population mean $\mu$ .

Question 18

If we have a sample size of 500 and a population proportion of 0.995,we can approximate the sampling distribution of $\hat { p }$ with a normal distribution.

Question 19

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

Question 20

The sampling distribution of $\bar { x }$ must be a normal distribution with a mean 0 and standard deviation 1.

Question 21

If we have a sample size of 100 and a population proportion of 0.10,the standard deviation of the sampling distribution of $\hat { p }$ Is ____.

A)10
B)9
C)0.03
D)3
E)90

Question 22

If we have a sample size of 100 and a population proportion of 0.10,the mean of the sampling distribution of $\hat { p }$ Is ____.

A)1000
B)10
C)1
D)0.10
E)0.01

Question 23

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)0.4207
B)0.9207
C)0.0793
D)0.4015
E)0.9015

Question 24

Exceed 94 kg is:

A)0.3413
B)0.8413
C)0.1587
D)0.5636
E)0.1687

Question 25

Suppose you take a sample of size 4 from a population with a mean of 70 and a standard deviation of 10.Based on such a sample,what are the mean and standard deviation of the sampling distribution of $\bar { x }$
?

A) $\mu _ { \bar { x } }$ = 70, $\sigma _ { \bar { x } }$ = 5
B) $\mu _ { \bar { x } }$ = 70, $\mu _ { \bar { x } }$ = 2.5
C) $\mu _ { \bar { x } }$ = 17.5, $\mu _ { \bar { x } }$ = 5
D) $\mu _ { \bar { x } }$ = 17.5, $\mu _ { \bar { x } }$ = 10
E)Cannot be determined unless the sample size is at least 30.

Question 26

The sample variance s² is an unbiased estimator of the population variance $\sigma ^ { 2 }$ .

Question 27

Be less than 84 kg is:

A)0.1687
B)0.9332
C)0.4332
D)0.0668
E)0.8413

Question 28

The central limit theorem states that if the sample size is sufficiently large,then the sampling distribution of the sample ________ is approximately normal,even if the sampled population is not normally distributed.

A)median
B)mode
C)standard deviation
D)variance
E)mean

Question 29

Consider a sampling distribution formed based on n = 9.If the standard deviation of the population of individual measurements is $\sigma$
,then the standard deviation of the population of all sample means $\sigma _ { \bar { x } }$
Equals ____.

A) $\frac { 1 } { 3 } \sigma$
B) $\frac { 1 } { 9 } \sigma$
C) $3 \sigma$
D) $9 \sigma$
E) $\frac { 1 } { 81 } \sigma$

Question 30

What is the probability that less than 64 patients will not be satisfied with the after-surgery care?

A)0.4772
B)0.0228
C)0.9772
D)0.9544
E)0.0197

Question 31

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

Question 32

As the sample size ______________ the variance of the sampling distribution of $\bar { x }$ ___________.

A)decreases,decreases
B)increases,remains the same
C)decreases,remains the same
D)increases,decreases
E)increases,increases

Question 33

For a finite population,the sampling distribution of the sample mean $\bar { x }$
can be developed by repeatedly taking all samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

Question 34

What are the mean and the standard deviation of the sampling distribution of $\hat { p }$
?

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

Question 35

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)the sample distribution of the sample mean is approximately normal.
E)the sample distribution of the sample mean is exactly normal.

Question 36

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

A)np ≥ 5
B)n(1 - p)≥ 5
C)np ≤ 5
D)n(1 - p)≤ 5 and np ≤ 5
E)np ≥ 5 and n(1 - p)≥ 5

Question 37

Whenever the sampled population has a normal distribution,the sampling distribution of $\bar { x }$ Is normal:

A)for only large sample sizes.
B)for only small sample sizes.
C)for any sample size.
D)for only samples of exactly 30.
E)for only samples of sizes greater than 31.

Question 38

What is the probability that at least 30 accounts will be classified as delinquent?

A)0.3186
B)0.1814
C)0.8186
D)0.6372
E)0.7584

Question 39

If the sampled population has a mean of 48 and standard deviation of 16,then for a sample of size n = 16 the sampling distribution of $\bar { x }$
Has a mean of ____ and a standard deviation of ____.

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

Question 40

The mean of the sampling distribution of $\bar { x }$ is always equal to the mean $\mu$ of the sampled population.

Question 41

What is the probability the mean length of the bolt is at most 3.1 cm?

A)0.8413
B)1
C)0.7157
D)0.2843
E)0.1587

Question 42

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

A)0399
B)0098
C)1700
D)0500
E)0813

Question 43

What is the probability the mean length of the bolt is at least 3.16 cm?

A)0.9772
B)0.0548
C)0.9452
D)0.4452
E)0.0228

Question 44

What are the mean and the standard deviation of the sampling distribution of $\hat { p }$ ?

A)0.16 and 0.0004
B)0.16 and 0.02
C)0.20 and 0.02
D)0.20 and 0.0004
E)0.20 and 0.16

Question 45

Suppose that 60 percent of the employees in a particular union support a candidate for union president.The probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 4 percentage points of the actual proportion is _____.

A)0.9786
B)0.9878
C)0.9902
D)0.5398
E)0.8413

Question 46

Suppose you take a random sample from a normally distributed population with mean $\mu$
= 16 and compute the sample mean $\bar { x }$
.If $\sigma _ { \bar { x } } ^ { 2 }$
= 4,find P( $\bar { x }$
< 25).

A)0300
B)1.000
C)1732
D)0577
E)8413

Question 47

What is the standard deviation of the sample mean?

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

Question 48

Suppose you take a sample of 40 observations from a uniform distribution.Based on this sample,the sampling distribution of
is _______.

Question 49

Suppose that 60 percent of the employees in a particular union support a candidate for union president.The probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 2 percentage points is _____.

A)0.9786
B)0.9878
C)0.9902
D)0.8030
E)0.8413

Question 50

Suppose you take a random sample from a normally distributed population with mean $\mu$ = 2500 and compute the sample mean )If $\sigma _ { \bar { x } } ^ { 2 }$ = 7,find P( $\bar { x }$ > 2510).

A)0000
B)9878
C)1732
D)0577
E)8413

Question 51

If we take a sample of size n = 100 from a population with $\mu$ = 400 and $\sigma$ = 20,find P(395.4 < $\bar { x }$ < 404.6).

A)0.9786
B)0.9878
C)0.1732
D)0.5398
E)0.8413

Question 52

The _____ says that if the sample size is sufficiently large,then the sample means are approximately normally distributed even if the sampled population is not normal.

Question 53

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

A)decreases;uniform
B)increases;normal
C)decreases;normal
D)increases;uniform
E)increases;exponential

Question 54

Suppose you take a random sample from a normally distributed population with mean $\mu$ = 175 and compute the sample mean $$\bar { x }$$ . If $$\sigma _ { \bar { x } } ^ { 2 }$$ = 9, find P( $$\bar { x }$$ > 172).

A)0300
B)0100
C)1732
D)0577
E)8413

Question 55

If we take a sample of size n = 100 from a population with $\mu$ = 400 and $\sigma$ = 200,find P( $\bar { x }$ < 402).

A)0764
B)9878
C)1732
D)5398
E)8413

Question 56

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

A)0399
B)0098
C)0170
D)0500
E)0813

Question 57

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

Question 58

What is the probability that at least 70 patients will not be satisfied with the after-surgery care?

A)0.8944
B)0.3944
C)0.1056
D)0.7888
E)0.8449

Question 59

If $\mu$ = 400,P( $\bar { x }$ < 396)=.0228,and n = 100,then the population standard deviation $\sigma$ Is _____.

A)76
B)98
C)17
D)20
E)41

Question 60

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

Question 61

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

Question 62

The sample mean is an unbiased,_______-variance point estimate of the population mean.

Question 63

The notation for the standard deviation of the sample mean is also known as the standard __________.

Question 64

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

Question 65

If the sampled population is finite and at least _____ times larger than the sample size,then the finite population multiplier is approximately equal to one.

Question 66

A golf tournament organizer is attempting to determine whether hole (pin)placement has a significant impact on the average number of strokes for the 13^thhole 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.

Question 67

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

Question 68

Suppose you take a random sample from a normally distributed population with mean

Question 69

The _________ theorem allows us to approximate the sampling distribution of a sample mean with a normal probability distribution whenever the sample size is sufficiently large.

Question 70

Packages of sugar bags for Sweeter Sugar Inc.have an average weight of 16 grams and a standard deviation of 0.2 grams.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 grams?

Question 71

As the sample size ___________,the variability of the sampling distribution of the sample proportion increases.

Question 72

Suppose you take a random sample of size n = 100 from a population with

Question 73

Suppose you take a random sample of size n = 100 from a population with

Question 74

Suppose you take a random sample of size n = 4 from a normally distributed population with

Question 75

The sampling distribution of the sample mean is approximately normal for sufficiently ________ sample sizes regardless of the distribution shape of the sampled population.

Question 76

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

Question 77

Suppose you take a random sample of size n = 100 from a population with

Question 78

Suppose you take a random sample of size n = 16 from a normally distributed population with

Question 79

The _______________________ of the sample mean
is the probability distribution of the population of all possible sample means that could be obtained from all possible samples of the same size.

Question 80

Suppose you take a random sample from a normally distributed population with mean