Probability and Statistics > Basic Statistics > Different Sampling Methods

## Different Sampling Methods: What’s the Difference: Overview

You’ll come across many terms in statistics that define different sampling methods: simple random sampling, systematic sampling, stratified random sampling and cluster sampling. How to tell the difference between the different sampling methods can be a challenge.

## Different Sampling Methods: How to Tell the Difference: Steps

**Step 1:** Find out if the study sampled from individuals (for example, picked from a pool of people). You’ll find **simple random sampling** in a school lottery, where individual names are picked out of a hat. But a more “systematic” way of choosing people can be found in “systematic sampling,” where every nth individual is chosen from a population. For example, every 100th customer at a certain store might receive a “doorbuster” gift.

**Step 2:** Find out if the study picked groups of participants. For large numbers of people (like the number of potential draftees in the Vietnam war), it’s much simpler to pick people by groups (**simple random sampling**). In the case of the draft, draftees were chosen by birth date, “simplifying” the procedure.

**Step 3:** Determine if your study contained data from more than one carefully defined group (“strata” or “cluster”). Some examples of strata could be: Democrats and Republics, Renters and Homeowners, Country Folk vs. City Dwellers, Jacksonville Jaguars fans and San Francisco 49ers fans. If there are two or more very distinct, clear groups, you have a **stratified sample** or a “cluster sample.” If you have data about the individuals in the groups, that’s a stratified sample. In order to perform stratified sampling on this sample, you could perform random sampling of each strata independently. If you only have data about the groups themselves (you may only know the location of the individuals), then that’s a **cluster sample**.

**Step 4:** Find out if the sample was easy to get. **Convenience samples** are like convenience stores: why go out of your way to get samples, when you can nip out to the corner store? A classic example of convenience sampling is standing at a shopping mall, asking passers by for their opinion.

The above steps walk you through the most common types of different sampling methods you’ll find in statistics. For a detailed list of all the types you’re likely to come across, see: Sampling techniques.

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Can you please help provide answers to these questions on statistics? I need to know how they got the answers.

Thank you.

Question 1

A sample of serum cholesterol levels of six men who visited a cholesterol screening clinic located in your city yielded values of

218, 273, 210, 259, 290, 232

The mean cholesterol level in this sample is

Answer

229.5

245.5

*247.0

266.0

Question 2

A researcher wants to determine how many individuals have health insurance. They decide to do a telephone survey using a list of telephone numbers that are subdivided into zip codes. It is determined that a representative sample from each zip code will be drawn. This type of sampling is:

Answer

cluster sampling.

systematic sampling.

stratified random sampling.

convenience sampling.

Question 3

What type of sampling is usually the easiest to do?

Answer

Quota sampling

Simple random sampling

* Convenience sampling

Cluster sampling

Question 4

All human blood can be typed as one of O, A, B, or AB. The distribution of the types varies a bit with race. Choose an African American at random. Here are the approximate probabilities that the person you choose will have blood type O, B, or AB.

Blood Type O A B AB

Probability 0.50 ? 0.20 0.05

The probability that the person chosen has blood type A is:

Answer

0.04

*0.25

0.27

0.95

Question 5

Which of the following variables is an example of the nominal level of measurement?

Answer

Rank in graduating class

Letter grade (i.e. A, B, C, D, or F)

Age of students

Amount of money earned

Question 6

Which variable would be considered to be measured at the ordinal level?

Answer

Religious affiliation

SAT score

Temperature

Severity of pain scale

Question 7

The characteristics of the normal distribution curve include the following except:

Answer

The total area under the curve represents 100% of all values.

The mean and median are found below the apex.

5% of the values lie beyond 2 standard deviations from the median.

The curve is not symmetrical.

All of the above.

Question 8

The ratio level of measurement would include which of the following?

Answer

Systolic blood pressure

Order of finishing test

Political affiliation

GRE score

Question 9

A scattergram can be used to display:

Answer

correlation.

causality.

nominal data.

categorical data.

Question 10

In a set of scores with a mean of 100 and a standard deviation of 15, what raw score is represented by a z score of 1.00?

Answer

115

130

100

70

Question 11

What is the median of 2, 2, 2, 3, 3, 5, 5, 6, 6,7?

Answer

5.5

6

4

41

Question 12

What is the range of 2, 12, 1, 10, and 22?

Answer

48

6

10

21

Question 13

How can descriptive statistics be defined?

Answer

Descriptive statistics describe the general characteristics of a distribution.

Descriptive statistics relate the data to a larger population.

Descriptive statistics develop the research question.

Descriptive statistics are identical to inferential statistics.

Question 14

In a normal distribution, what percentage of scores fall between the mean and a z score of +1.00?

Answer

16%

34%

50%

95%

Question 15

When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using which of the following?

Answer

Inductive statistics

Deductive statistics

Descriptive statistics

Inferential statistics

Question 16

What can you conclude if the obtained value of a test statistic exceeds the critical value?

Answer

The null hypothesis cannot be rejected.

You made an error when calculating the test statistic.

The null hypothesis can be rejected.

Your obtained value is not statistically significant.

Question 17

Which is the strongest correlation?

Answer

+ 0.76

+ 0.21

– 0.01

– 0.88

Question 18

If you calculated a correlation coefficient of .35, how would you describe this value?

Answer

Moderate

Weak

Very strong

Very weak

Question 19

Emergency room physicians at four hospitals (who serve very different median income geographic areas) hypothesized that children who arrive at the emergency room after swallowing objects are at increased risk of elevated blood lead levels. Four groups of thirty-five children each are selected from each hospital who presented with foreign bodies in their gastrointestinal tract were screened for blood lead levels. The mean was 15.7 ug/dL for group 1, 14 ug/dL for group 2, 10 ug/dL for group 3, and 20 ug/dL for group 4. They believe that there will be a significant difference among groups. The best statistical test to use for this study is the:

Answer

ANOVA test.

Chi-square test.

student t-test.

regression analysis test.

Question 20

The county health department in your geographic area would like to know how many children who live in the county are being immunized by doctors or by the county health department. A comparison is wanted of children younger than 2 years of age who use the county health department services with those who don’t. A county health survey is conducted, which interviewed a random sample of 42,000 children younger than 2 years of age. The population of the survey would be:

Answer

the 42,000 children younger than 2 years of age in your county.

all people who use health services in your county.

all people who do not use health services in your area county.

all children younger than 2 years of age in your county.

Question 21

In 10 randomly sampled children referred for recurrent episodes of ear aches the mean number of times the children went swimming in a week was 10 times. Assume the swimming data is normally distributed. What type of statistical test would be best to use in this situation to determine if there is a difference in the mean number of times children went swimming between the healthy population and the 10 randomly sampled children?

Answer

Student’s t-test

ANOVA test

Chi-square test

Regression test

Question 22

Studying the association between blood cholesterol levels and changes in blood pressure, a researcher would obtain the most effective use of the data by the application of:

Answer

student’s t-test.

f-test.

Chi-square test.

analysis of variance.

correlation analysis.

Question 23

The correlation between the age and height of children is found to be about r = y of the child. We conclude:

Answer

the least squares regression line of y on x would have a slope of 0.7.

the fraction of the variation in heights explained by the least squares regression line of y on x is 0.49.

about 70% of the time, age will accurately predict height.

height is generally 70% of child’s age.

Question 24

To assess the possible association between tobacco use and the subsequent development of lung cancer, a total of 135 patients were studied. The results were as follows:

Lung Cancer (+) No Lung Cancer (-) Total

Used Tobacco (+) 36 31 67

Did Not Use Tobacco (-)22 46 68

Total 58 77 135

The most appropriate test to use in comparing the proportion of cancer patients who used tobacco to those who did not and subsequent development of lung cancer is:

Answer

Chi-square test.

ANOVA test.

t-test.

correlation test.

Question 25

In a study at a school, the mean systolic blood pressure of 250 medical students was 116 mm Hg, with a standard deviation of 4 mm Hg. From the data, 99.7% of the medical students will have systolic blood pressures (mm Hg) in the range of:

Answer

110-130

104-128

112-120

116-124

Can you please help provide answers to these questions on statistics? I need to know how they got the answers.

Thank you.

Question 1

A sample of serum cholesterol levels of six men who visited a cholesterol screening clinic located in your city yielded values of

218, 273, 210, 259, 290, 232

The mean cholesterol level in this sample is

Answer

229.5

245.5

*247.0**

266.0

Question 2

A researcher wants to determine how many individuals have health insurance. They decide to do a telephone survey using a list of telephone numbers that are subdivided into zip codes. It is determined that a representative sample from each zip code will be drawn. This type of sampling is:

Answer

cluster sampling.

systematic sampling.

stratified random sampling.***

convenience sampling.

Question 3

What type of sampling is usually the easiest to do?

Answer

Quota sampling

Simple random sampling

* Convenience sampling****

Cluster sampling

Question 4

All human blood can be typed as one of O, A, B, or AB. The distribution of the types varies a bit with race. Choose an African American at random. Here are the approximate probabilities that the person you choose will have blood type O, B, or AB.

Blood Type O A B AB

Probability 0.50 ? 0.20 0.05

The probability that the person chosen has blood type A is:

Answer

0.04

*0.25***

0.27

0.95

Question 5

Which of the following variables is an example of the nominal level of measurement?

Answer

Rank in graduating class

Letter grade (i.e. A, B, C, D, or F)****

Age of students

Amount of money earned

Question 6

Which variable would be considered to be measured at the ordinal level?

Answer

Religious affiliation

SAT score

Temperature

Severity of pain scale****

Question 7

The characteristics of the normal distribution curve include the following except:

Answer

The total area under the curve represents 100% of all values.

The mean and median are found below the apex.

5% of the values lie beyond 2 standard deviations from the median.

The curve is not symmetrical.****

All of the above.

Question 8

The ratio level of measurement would include which of the following?

Answer

Systolic blood pressure***

Order of finishing test

Political affiliation

GRE score

Question 9

A scattergram can be used to display:

Answer

correlation.***

causality.

nominal data.

categorical data.

Question 10

In a set of scores with a mean of 100 and a standard deviation of 15, what raw score is represented by a z score of 1.00?

Answer

115***

130

100

70

Question 11

What is the median of 2, 2, 2, 3, 3, 5, 5, 6, 6,7?

Answer

5.5

6

4**

41

Question 12

What is the range of 2, 12, 1, 10, and 22?

Answer

48

6

10

21**

Question 13

How can descriptive statistics be defined?

Answer

Descriptive statistics describe the general characteristics of a distribution.***

Descriptive statistics relate the data to a larger population.

Descriptive statistics develop the research question.

Descriptive statistics are identical to inferential statistics.

Question 14

In a normal distribution, what percentage of scores fall between the mean and a z score of +1.00?

Answer

16%

34%***

50%

95%

Question 15

When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using which of the following?

Answer

Inductive statistics

Deductive statistics

Descriptive statistics

Inferential statistics****

Question 16

What can you conclude if the obtained value of a test statistic exceeds the critical value?

Answer

The null hypothesis cannot be rejected.

You made an error when calculating the test statistic.

The null hypothesis can be rejected.***

Your obtained value is not statistically significant.

Question 17

Which is the strongest correlation?

Answer

+ 0.76

+ 0.21

– 0.01

– 0.88**

Question 18

If you calculated a correlation coefficient of .35, how would you describe this value?

Answer

Moderate***

Weak

Very strong

Very weak

Question 19

Emergency room physicians at four hospitals (who serve very different median income geographic areas) hypothesized that children who arrive at the emergency room after swallowing objects are at increased risk of elevated blood lead levels. Four groups of thirty-five children each are selected from each hospital who presented with foreign bodies in their gastrointestinal tract were screened for blood lead levels. The mean was 15.7 ug/dL for group 1, 14 ug/dL for group 2, 10 ug/dL for group 3, and 20 ug/dL for group 4. They believe that there will be a significant difference among groups. The best statistical test to use for this study is the:

Answer

ANOVA test.***

Chi-square test.

student t-test.

regression analysis test.

Question 20

The county health department in your geographic area would like to know how many children who live in the county are being immunized by doctors or by the county health department. A comparison is wanted of children younger than 2 years of age who use the county health department services with those who don’t. A county health survey is conducted, which interviewed a random sample of 42,000 children younger than 2 years of age. The population of the survey would be:

Answer

the 42,000 children younger than 2 years of age in your county.

all people who use health services in your county.

all people who do not use health services in your area county.

all children younger than 2 years of age in your county.****

Question 21

In 10 randomly sampled children referred for recurrent episodes of ear aches the mean number of times the children went swimming in a week was 10 times. Assume the swimming data is normally distributed. What type of statistical test would be best to use in this situation to determine if there is a difference in the mean number of times children went swimming between the healthy population and the 10 randomly sampled children?

Answer

Student’s t-test***

ANOVA test

Chi-square test

Regression test

Question 22

Studying the association between blood cholesterol levels and changes in blood pressure, a researcher would obtain the most effective use of the data by the application of:

Answer

student’s t-test.

f-test.

Chi-square test.

analysis of variance.

correlation analysis.

Question 23

The correlation between the age and height of children is found to be about r = y of the child. We conclude:

Answer

the least squares regression line of y on x would have a slope of 0.7.

the fraction of the variation in heights explained by the least squares regression line of y on x is 0.49.****

about 70% of the time, age will accurately predict height.

height is generally 70% of child’s age.

Question 24

To assess the possible association between tobacco use and the subsequent development of lung cancer, a total of 135 patients were studied. The results were as follows:

Lung Cancer (+) No Lung Cancer (-) Total

Used Tobacco (+) 36 31 67

Did Not Use Tobacco (-)22 46 68

Total 58 77 135

The most appropriate test to use in comparing the proportion of cancer patients who used tobacco to those who did not and subsequent development of lung cancer is:

Answer

Chi-square test.

ANOVA test.

t-test.

correlation test.

Question 25

In a study at a school, the mean systolic blood pressure of 250 medical students was 116 mm Hg, with a standard deviation of 4 mm Hg. From the data, 99.7% of the medical students will have systolic blood pressures (mm Hg) in the range of:

Answer

110-130

104-128****

112-120

116-124

A principal told his faculty that the ABC test, the PALS test, and the Sesame Street test could be used to predict whether or not a student passed their 3rd grade Reading SOL test. When one of the teachers asked him how he knew this, he said that he read an article that showed that the reliability of those three tests on the 3rd grade Reading SOL test was α =.437. Was he correct? Explain.