Deck 5: Sampling Distributions

Question 1

A gumball machine has three colours of gumballs. There are 10 red gumballs, 10 blue gumballs, and 20 white gumballs. What is the probability of selecting a red gumball when picking a gumball at random from the machine?

A) .25
B) .50
C) .75
D) none of these

Answer 1

A

Question 2

A gumball machine contains three colours of gumballs. There are 10 red gumballs, 10 blue gumballs, and 20 white gumballs. If you take a random sample of four gumballs from the machine and three are white, what is the probability that the fourth will be blue?

A) .25
B) .50
C) .75
D) none of these

Answer 2

A

Question 3

If you had 5 total employees, how many different draws of 3 employees are possible from this population when drawing random samples?

A) 15
B) 45
C) 60
D) none of these

Answer 3

C

Question 4

When sampling customers, you can increase the representativeness of your sample by ______.

A) drawing from a larger population
B) drawing from a smaller population
C) collecting a smaller sample
D) collecting a larger sample

Question 5

The population standard error of the mean is ______.

A) the z-score of the population mean
B) the z-score of the population standard deviation
C) the standard deviation of all possible sample means
D) the mean of all possible sample standard deviations

Question 6

x̄ appears in the subscript of the population standard error of the mean because it represents ______.

A) the mean of the standard deviations
B) the standard deviation of the means
C) the standard deviation of the standard deviations
D) the mean of the means

Question 7

If you randomly select a sample of n = 50 and a sample of n = 100 from the sample population, which one would you assume to be more representative of the population?

A) n = 50
B) n = 100
C) neither; they are equally accurate
D) none of these

Question 8

Sampling error occurs because ______.

A) the researcher made a mistake
B) the researcher chose an inappropriate sample
C) of chance factors
D) of a poorly designed study

Question 9

If you used simple random sampling to select n = 2 when N = 10, the first selected subject has a ______ chance of being selected.

A) 10%
B) 20%
C) 50%
D) none of these

Question 10

If you wanted to ensure you have an equal number of men and women in your sample, you could use ______.

A) simple random sampling
B) stratified random sampling
C) convenience sampling
D) all of these

Question 11

You want to select a random sample of employees from your organization, but you need to ensure that there are equal proportions of people from each department. Each department would be considered a ______.

A) condition
B) random sample
C) convenience sample
D) stratum

Question 12

In order to use stratified random sampling, you must ______.

A) randomly select individuals from your population
B) identify appropriate strata, then randomly select strata to be included
C) identify appropriate strata, then ask for volunteers within strata
D) identify appropriate strata, then randomly selection within strata

Question 13

You want to ensure that the five departments in your organization are equally represented in your sample. You need 100 responses to your surveys. How many people from each department should be in your sample?

A) 5
B) 20
C) 100
D) none of these

Question 14

You want to ensure that the composition of your sample of employees has the same balance of men and women that your organization has. Your organization is 60% women and 40% men. If you need 100 responses to your surveys, how many women are in your population?

A) 40
B) 60
C) 100
D) none of these

Question 15

You want to ensure that the composition of your sample of employees has the same balance of salespeople, customer service representatives, and warehouse workers that your organization has. Your organization has 20 salespeople, 30 customer service representatives, and 50 warehouse workers. If you need 50 total responses to your survey, how many warehouse workers should you ask to respond?

A) 25
B) 30
C) 50
D) none of these

Question 16

A possible concern with convenience sampling is ______.

A) your sample may not be drawn from your population of interest
B) the sample may be biased
C) you cannot ensure your sample is representative of your population
D) all of these

Question 17

You should use convenience sampling when ______.

A) you want a larger sample
B) you are unable to use stratified random sampling
C) you are unable to use simple random sampling
D) both b and c

Question 18

If we create a distribution of all possible sample means given a particular sample size, we have created a(n) ______.

A) estimate of the population standard error
B) normal distribution
C) sampling distribution
D) Poisson distribution

Question 19

If you change the size of the sample ______.

A) the standard error will change
B) the sampling distribution will change
C) n will change
D) all of these

Question 20

If n = 4 and $\sigma$ = 2, the population standard error is ______.

A) 0.5
B) 1.0
C) 2.0
D) 8.0

Question 21

If n = 25 and s² = 16, the sample estimate of the standard error is ______.

A) 0.80
B) 0.64
C) 0.31
D) 0.16

Question 22

If s = 10 and n = 100, we would expect that 68% of sample means would fall between ______.

A) ±1
B) ±0.1
C) ±2
D) ±0.2

Question 23

If $\sigma$ ² = 36 and n = 9, we would expect that 95% of sample means would fall between ______.

A) ±2
B) ±4
C) ±8
D) ±12

Question 24

If x̄ = 10 and $\mu$ = 12, then 2 is the ______.

A) variance
B) standard deviation
C) standard error
D) sampling error

Question 25

You should use the sample estimate of the standard error instead of the population standard error when ______.

A) the sample standard deviation is easier to calculate than the population standard deviation
B) the sample standard deviation is unknown
C) the population standard deviation is unknown
D) any time; they are the same

Question 26

If you sample standard error equals .25, this means that ______.

A) on average, sample means fall within 25% of the population mean
B) on average, sample means fall within .25 of the population mean
C) on average, sample means fall within .5 of the population mean
D) none of these

Question 27

You know that the sampling distribution of all means for a given sample size will be approximately normally distributed because of the ______.

A) assumptions of the uniform distribution
B) central tendency
C) central limit theorem
D) population standard error of the mean

Question 28

In a sampling distribution, what percentage of sample means should fall within ±1 standard error of the population mean?

A) 34%
B) 68%
C) 95%
D) none of these

Question 29

If you randomly select five subjects from a population, you are sampling.

Question 30

Increasing sample size will guarantee a more representative sample of the population.

Question 31

A good sample will perfectly reflect the population.

Question 32

The sample mean estimates the population mean.

Question 33

If possible, it is always preferable to measure a parameter instead of a statistic.

Question 34

You are more likely to draw an accurate conclusion when n = 20 than when n = 100.

Question 35

Sampling error exists with only some types of statistics.

Question 36

$\sigma_{x}^{-}$ represents the population standard error of the mean.

Question 37

If $\mu$ = 10, all sample means should also equal 10.

Question 38

Sampling error should be avoided at all costs.

Question 39

If you have complete access to sample your population, simple random sampling is the best method to use.

Question 40

If you have more than a single group of interest, you can use stratified random sampling to ensure an equal representation of all groups in your sample.

Question 41

If you want to sample equally between five locations of your company, you should identify more than five strata.

Question 42

Simple random sampling is the second step of stratified random sampling.

Question 43

If 30% of your population works at Plant A, 30% work at Plant B, and 40% work at Plant C, 60 people from Plant A and Plant B should be included in a stratified random sample.

Question 44

It is difficult to use a true random sample in real-world settings.

Question 45

When using convenience sampling, you can never be sure that your sample represents your population.

Question 46

When n > 100, the sampling distribution will likely be normally distributed.

Question 47

Larger sample sizes lead to smaller standard errors.

Question 48

Explain the difference between random sampling and stratified random sampling. Provide an example of each.

Question 49

Explain when convenience sampling should be used. Provide one benefit and one drawback.

Question 50

Define sample standard error in terms of both sample means and the sampling distribution.

Question 51

Describe the central limit theorem and explain what we can assume about the sampling distribution based upon this principle.

Question 52

Consider the sample collected for the survey variable below for Questions.

-What is the standard deviation of the survey variable?

Question 53

Consider the sample collected for the survey variable below for Questions.

-What is the sample estimate of the standard error of the survey variable?

Question 54

Consider the sample collected for the survey variable below for Questions.

-How would you interpret the sample estimate of the standard error you calculated above?

Question 55

Consider a business with 4 employees. List the composition of all possible draws when randomly selecting employees for samples of n = 3.

Question 56

You are interested in conducting a survey of your employees, but you want to ensure that men and women are appropriately represented in your sample. In your organization, 70% of your employees are women and 30% are men. If you used stratified random sampling appropriately, how many men and women would be in your sample of 150 employees?