Chapter 8

Question 1

What is random sampling difference?

Answer 1

Random sampling refers to the process of selecting a sample from a population so that every individual or item has an equal chance of being chosen.

This technique is crucial in ensuring that the sample is representative of the population, thereby helping to minimize bias in research and statistical analysis.

Question 2

Differentiate between a parameter and a statistic.

Answer 2

Parameter: A summary value (e.g., mean, variance, standard deviation, etc.) of a population of observations

Statistic: A summary value of a sample

Question 3

Differentiate between descriptive and inferential statistic.

Answer 3

1. Specifying the population of interest
2. Collecting all observations from the population
3. Computing summary values (parameters), such as the mean and standard deviation
4. Using these summary values to describe the properties of the population

Inferential statistics require
1. Obtaining one or more samples from the population(s) of interest
2. Computing estimates of parameters from the sample data
3. Making inferences about the corresponding population parameters from
which the sample was drawn

Question 4

What is summary fluctuation?

Answer 4

Sampling fluctuation: Refers to the fact that samples drawn from the same
population will yield summary measures that vary; variability of these measures
depends on sample size

Question 5

How do we infer the population mean?

Answer 5

• Sample means fluctuate
• Sample the population over and over and see how frequently each mean occurs

Question 6

How to construct the random sampling distribution?

Answer 6

▪ Repeatedly draw samples from a population
▪ Sample size is the same every time (e.g., IQ scores n = 10)
▪ Calculate the mean (or some other statistic) of each sample
▪ Do this until you have calculated the mean of all possible
samples
▪ Calculate the relative frequencies

Question 7

What happens when the size of each
sample increases and as the number of samples increases?

Answer 7

RSD of sample means (or other statistics)
▪ Approaches the shape of a normal distribution as size of each
sample increases and as number of samples increase

Question 8

The mean of the random sampling distribution of the mean
mean of the raw score population (m). True or false?

Answer 8

True

Question 9

What happens to the variance of the RSD when the sample size increases?

Answer 9

As the sample size increases, the variance of the random sampling distribution of the mean decreases.

Question 10

What is standard error?

Answer 10

Standard error: Standard deviation of a random sampling distribution

Question 11

Compared to the distribution of individual raw scores, will the distribution of the sample means have more or less variability? Explain your answer.

Answer 11

The distribution of sample means will have less variability than the distribution of individual raw scores, and this is particularly true as the sample size increases. The sample means become more consistent and centered around the population mean as the sample size grows.

Question 12

What is the shape of the distribution of the sample mean? Does it depend on the shape of the distribution of the individual raw scores?

Answer 12

The shape of the distribution of sample means is mostly normal for large sample sizes due to the Central Limit Theorem, regardless of the population’s shape.

For small sample sizes, the shape of the sample means will resemble the shape of the original population distribution.

Question 13

Does the mean of the distribution of sample means differ from the mean of the
distribution of the individual raw scores?

Answer 13

No, the mean of the distribution of sample means is the same as the mean of the distribution of individual raw scores.

So, while the variability of the sample means is less than the variability of the raw scores, the mean remains unchanged.

Question 14

What is the central limit theorem?

Answer 14

1. The random sampling distribution of the mean tends toward a normal dis
   contribution, irrespective of the shape of the original raw score population.
2. This tendency increases as sample size increases.

Question 15

how to calculate the random sampling distribution of difference?

Answer 15

T
Step 1. Randomly draw one sample with replacement, of a fixed size, from
each of two populations with equal means. (The two samples don’t have to
be of equal size.)
Step 2. Calculate the mean of each sample and record the difference.
Step 3. Repeat Steps 1 and 2 until all possible pairs of samples have been drawn.
Step 4. Place the mean differences in a relative frequency distribution.

Question 16

Mean of all the differences from the samples equal what?

Answer 16

zero