Sampling and sampling distribution

Question 1

What is sampling ?

Answer 1

• the process of selecting units from a population of interest
• by studying sample goal is to generalize back to the population

Question 2

What are the 2 types of samples?

Answer 2

1. Non probability sampling: all individuals in the pop don’t have an equal/determined chance of being selected
2. Probability sampling: everyone in the pop has equal chance of being selected; findings can be generalised to the population

Question 3

When is a snowball sample appropriate?

Answer 3

when the members of a population are difficult to locate

Question 4

What is a simple random sample?

Answer 4

• each unit of target population is assigned random number
• set of random numbers is generated
• units having those numbers are selected

Question 5

What is a parameter?

Answer 5

a measure used to describe a population distribution

Question 6

What’s a statistic?

Answer 6

A measure used to describe a sample distribution

Question 7

What are the following notations?
mean
proportion
standard deviation
variance

Answer 7

Mean: Sample x̄ Population μ
Proportion: Sample p Population π
Standard deviation: Sample S Population σ
Variance: Sample S² Population σ²

Question 8

What is sampling error?

Answer 8

the discrepancy between a sample estimate of a population parameter (statistic) and the real population parameter

Question 9

What is a dilemma?

Answer 9

• Since we don’t know the population parameter, how do we know whether our statistics are accurate representations of the population
• the sampling distribution allows us to compare our sample with others and determine the likelihood that it represents the population

Question 10

what is the sampling distribution?

Answer 10

• the theoretical distribution of all possible sample values with exactly the same sample size
  eg. sampling distribution of the mean/ sampling distribution of the median

Question 11

what is the central limit theorem?

Answer 11

If all possible random samples of size N are drawn from a population with mean μ and a standard deviation σ, then as N becomes larger, the sampling distribution of sample means becomes approximately normal, with mean μ and SD σ/ √N

Question 12

What is the sampling distribution of the mean?

Answer 12

probability distribution of sample means that would be obtained by drawing from the population, all possible samples of the same size

Question 13

What is standard error?

Answer 13

• the standard deviation of the sampling distribution
• describes how much dispersion there is in the sampling distribution of the mean
• as sample size gets larger the standard error gets smaller > larger sample can better represent the population and more accurately infer the parameter

Question 14

Is the central limit theorem affected by skewness of distribution?

Answer 14

No, it holds true regardless of whether the source population is normal or skewed, if the sample size is sufficiently large