Deck 7: Sampling and Sampling Distributions

Question 1

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

Answer 1

True

Question 2

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 2

True

Question 3

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.

Answer 3

True

Question 4

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

Question 5

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

Question 6

The Central Limit Theorem states that as sample size increases,the population distribution more closely approximates a normal distribution.

Question 7

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

Question 8

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 9

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

Question 10

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

Question 11

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 12

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 13

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

Question 14

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

Question 15

The standard deviation of the sampling distribution of the sample mean is σ.

Question 16

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

Question 17

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

Question 18

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 19

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

Question 20

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

Question 21

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

A) μ
B) μ/√n
C)
D) z

Question 22

Whenever the population has a normal distribution,the sampling distribution of is a 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 23

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 ≥ 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 24

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 σ.

A) always
B) sometimes
C) never

Question 25

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

Question 26

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 27

____________ 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) The Central Limit Theorem

Question 28

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 29

If the sample size n is infinitely large,then s² is an unbiased estimator of σ².

Question 30

According to the Central Limit Theorem,if a sample size is at least _____,then for most sampled populations,we can conclude that the sample means are approximately normal.

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

Question 31

The Central Limit Theorem states that as the sample size increases,the distribution of the sample ____________ approaches the normal distribution.

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

Question 32

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

A)
B) σx
C)
D) μ

Question 33

There is no easy way to calculate an unbiased point estimate of σ.

Question 34

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 other choices is correct.

Question 35

If the sampled population is finite and at least _____ times larger than the sample size,we treat the population as infinite.

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

Question 36

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 mean must equal the population mean,the sample mean must equal the population mean for large samples,and the sample standard deviation must equal the population standard deviation.
E) None of the other choices is correct.

Question 37

The quantity √[(N − n)(N − 1)] is called the finite population multiplier.

Question 38

If the sampled population has a mean of 48 and standard deviation of 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 39

For nonnormal 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 40

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

A) μ
B) p
C) p × n
D) (1 − p)

Question 41

A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5.The sampling distribution of ____________________.

A) cannot be determined
B) is skewed to the left
C) is approximately normal
D) is skewed to the right

Question 42

Find P( < 35)if μ = 40,σ_x = 16,n = 16.

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

Question 43

An unbiased estimate of σ² is _____.

A) s
B) s²
C)
D) σ

Question 44

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 of Sample Mean
C) probability
D) observations

Question 45

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 46

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 packages 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 47

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 _______________.

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

Question 48

A golf tournament organizer is attempting to determine whether hole (pin)placement has a significant impact on the average number of strokes for the 13th 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 49

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 50

A random sample of size 1,000 is taken from a population where p = .20.Describe the sampling distribution of .

A) cannot be determined
B) approximately normal
C) skewed to the left
D) skewed to the right

Question 51

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

A) population
B) random
C) observed
D) sample

Question 52

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