Topic 6 - Sampling

Question 1

What is a simple random sample

Answer 1

• Every object in the population has an equal chance of being selected
• Objects are selected independently

Question 2

What is the ideal sample method that others are compared to

Answer 2

• Simple random sampling

Question 3

What is a sampling distribution

Answer 3

• The distribution of all the possible values of a statistic for a random sample of size ‘n’ selected from a population

Question 4

What is the “sampling distribution of the sample mean”

Answer 4

• A distribution formed when we take multiple samples of a given size from a population and calculate the sample mean, and then make a distribution from these means

Question 5

What are the properties of the mean and variance of sampling distributions and population

Answer 5

• The mean of the sampling distribution of the sample means is the same as the population mean
• The variance of the sampling distribution of the sample means is not the same as the population variance -> Var(X bar) = Var(X) / n

Question 6

What is the standard error of the mean

Answer 6

• A measure of variability in the mean from sample to sample
• As the sample size increases, SE will increase

Question 7

How is the standard error of the mean calculated

Answer 7

• Standard error (sigma x bar) = Var(X) / sqrt(n)

Question 8

When are individual sample members not distributed independently of one another

Answer 8

• If n is not a small fraction of the population N (typically, n is more than 5% of N)

Question 9

What needs to be used if n is more than 5% of N

Answer 9

• A finite population correction
• Var(X bar) = Var / n * N - n / N - 1
• N - n / N - 1 is called the finite population correction factor
• Only applied to variance and S.D

Question 10

what does n denote

Answer 10

• The sample size for each mean
• not the number of samples, this is assumed to be infinite

Question 11

How large does our sample need to be for the CLT to apply

Answer 11

• n > 25 typically
• If the population is normal then the distribution will automatically be normal

Question 12

How is the sample variance denoted

Answer 12

• s^2

Question 13

How is the sample variance calculated

Answer 13

• s^2 = 1 / n - 1 * sum of (xi - x bar)

Question 14

What is E(s^2)

Answer 14

• the mean of s^2 = σ^2

Question 15

What does it mean if a population distribution is normal

Answer 15

• μ bar = μ
• σ^2 bar = σ^2 / n

Question 16

What can we infer if the population is not normal

Answer 16

• We can still apply the central limit theorm
• μ bar = μ
• σ^2 bar = σ^2 / n

Question 17

If the population distribution is normal, how can s^2 be used for a chi squared distribution

Answer 17

• chi^2 = (n-1)s^2 / σ^2 with n-1 degrees of freedom