Sampling Distributions, Standard Error and Confidence Intervals

Question 1

What is the process of selecting a smaller group from a larger group called?

Answer 1

Sampling

Sampling allows researchers to study characteristics of a population without examining the entire group.

Question 2

What does inferential statistics use to make predictions about a population?

Answer 2

Sample data

Inferential statistics allows conclusions to be drawn about a whole population based on a sample.

Question 3

What is the difference between a population and a sample?

Answer 3

A population is the entire group of interest, while a sample is a subset selected to represent that population.

Question 4

What is one key characteristic of a good quantitative sample?

Answer 4

Representativeness

The sample must accurately reflect the population’s key characteristics.

Question 5

What is a critical method to minimize bias in sample selection?

Answer 5

Random selection

Ensures each member of the population has an equal chance of being selected.

Question 6

What is the recommended sample size for the sampling distribution of the mean to approximate normality?

Answer 6

Approximately 30

This is suggested by the Central Limit Theorem.

Question 7

What is a sampling frame?

Answer 7

A list of individuals or objects used to select a sample for a research study.

Question 8

Name one reason why biases can occur in sampling frames.

Answer 8

Incomplete or outdated sampling frame

Missing members of the population can lead to unrepresentative samples.

Question 9

What method of sampling involves selecting individuals at regular intervals?

Answer 9

Systematic Random Sampling

This method uses a calculated sampling interval.

Question 10

What is the definition of sampling error?

Answer 10

The difference between a sample statistic and the true population parameter due to random variation.

Question 11

What does standard error (SE) measure?

Answer 11

The expected variation of a sample statistic from sample to sample due to sampling error.

Question 12

What is a sampling distribution?

Answer 12

The probability distribution of a sample statistic obtained from many same-size random samples.

Question 13

According to the Central Limit Theorem, what happens to the sampling distribution if the sample size is sufficiently large?

Answer 13

It will be approximately normal regardless of the population distribution.

Question 14

What is the minimum sample size typically required for the Central Limit Theorem to apply?

Answer 14

n ≥ 30

Samples of this size tend to produce a normal distribution of sample means.

Question 15

What happens to the sampling distribution if the population distribution is normal?

Answer 15

The sampling distribution of the sample statistic will also be normal, regardless of sample size.

Question 16

True or False: Sampling error can be completely eliminated in a study.

Answer 16

False

Sampling error is unavoidable when using a sample.

Question 17

What is the advantage of stratified random sampling?

Answer 17

Each stratum is represented in the sample, increasing accuracy of estimates.

Question 18

What is a disadvantage of simple random sampling?

Answer 18

It may not be feasible for large populations.

Question 19

What is cluster sampling?

Answer 19

Sampling method where clusters are selected randomly, and either everyone in the clusters is surveyed or a random sample is taken.

Question 20

What does the Central Limit Theorem state about the distribution of sample means?

Answer 20

The distribution of those averages will be normal regardless of the original population distribution

This is true as long as random samples of a certain size are taken.

Question 21

What is the significance of taking many samples (k ≥ 1000) in the context of the Central Limit Theorem?

Answer 21

It leads to normally distributed sampling distributions even when the sample size is very small (n ≤ 5).

Question 22

What is the standard error (SE)?

Answer 22

It quantifies the expected variability of a sample mean (or proportion) from the true population mean (or proportion).

Question 23

How is the standard error (SE) calculated for the mean?

Answer 23

SE = sample standard deviation (SD) / √n, where n is the sample size.

Question 24

True or False: The standard error (SE) gets larger as the sample size increases.

Answer 24

False.

Question 25

What does a smaller standard error (SE) indicate about the sample mean's accuracy?

Answer 25

The sample mean is more likely to be a good estimate of the population mean.

Question 26

What is the purpose of calculating the standard error (SE)?

Answer 26

To quantify how much we expect the sample mean (or proportion) to differ from the true population parameter due to sampling variation.

Question 27

What is a confidence interval (CI)?

Answer 27

A statistical tool used to estimate a range of values likely to contain an unknown population parameter based on a sample.

Question 28

What is the typical level of confidence used for confidence intervals?

Answer 28

95%.

Question 29

How is a confidence interval calculated?

Answer 29

CI = sample statistic ± (critical value × SE).

Question 30

What does the notation ± 1.96 represent in the context of confidence intervals?

Answer 30

It corresponds to the z-scores for a 95% confidence level.

Question 31

Fill in the blank: The standard error of the proportion is calculated using the formula SE = _______.

Answer 31

√[p(1-p)/n].

Question 32

What does it mean when confidence intervals for two groups overlap?

Answer 32

There is no statistically significant difference between the means of the two groups.

Question 33

What is the relationship between sample size and standard error (SE)?

Answer 33

As the sample size increases, the standard error decreases.

Question 34

What does the term 'sampling variation' refer to?

Answer 34

The differences in estimates that occur due to the random selection of samples.

Question 35

What is the formula for the confidence interval for the mean?

Answer 35

CI = sample mean ± (critical value × SE of the mean).

Question 36

What does it mean to be '95% confident' in a confidence interval?

Answer 36

If we take many samples, 95% of the confidence intervals calculated will contain the true population parameter.

Question 37

What is the implication of a confidence interval that does not overlap with another?

Answer 37

The difference is likely true in the population.

Question 38

What is the purpose of conducting hypothesis testing in relation to confidence intervals?

Answer 38

To make stronger claims about the difference between the means of two groups.

Question 39

How can we calculate the confidence interval for a proportion?

Answer 39

Using the formula: CI = sample proportion ± (1.96 × SE of the proportion).

Question 40

What does the standard deviation (SD) represent in the context of confidence intervals?

Answer 40

It measures the variability of the sample data.

Question 41

What is the significance of the sample size being n ≥ 30 in the Central Limit Theorem?

Answer 41

It ensures that the sampling distribution of the sample mean tends to normality.

Question 42

What does the standard error help estimate?

Answer 42

Uncertainty in a sample’s mean.

Question 43

True or False: The Central Limit Theorem only applies when multiple samples are taken.

Answer 43

False.