Chapter 9 ~ Sampling Distributions

Question 1

Statistic

Answer 1

A number that can be computed from the sample data without making use of any unknown parameters. In practise, we often use a statistic to estimate an unknown parameter.

Question 2

What is the symbol for a population mean?

Answer 2

μ (mu)

Question 3

What is the symbol for mean of a sample?

Answer 3

x̄ (x-bar)

Question 4

Sampling Variability

Answer 4

The value of a statistic varies in repeated sampling. This is not fatal!

Question 5

What is the symbol for a population proportion?

Answer 5

p

Question 6

What is the symbol for a sample proportion?

Answer 6

p̂ (p-hat)

Question 7

Sampling distribution

Answer 7

The distribution of values taken by the statistic in all possible samples of the same size from the same population.

Question 8

Bias

Answer 8

The centre of the sampling distribution is not equal to the true value of the parameter.

Question 9

Variability of a statistic

Answer 9

Described by the spread of its sampling distribution. This spread is determined by the sampling design and the size of the sample.
Larger samples –> smaller spread

Question 10

What is the mean of the sampling distribution of p̂?

Answer 10

Exactly p

Question 11

What is the standard deviation of the sampling distribution of p̂?

Answer 11

Sqrt(pq/n)

Question 12

When can you use the formula for the standard deviation of p̂?

Answer 12

ONLY when the population is at least 10 times as large as the sample. (N≥10n)

Question 13

What conditions must be satisfied to use the Normal approximation for the sampling distribution of p̂?

Answer 13

np≥10 and nq≥10

Question 14

What is the mean of the sampling distribution of x̄?

Answer 14

Exactly μ

Question 15

What is the standard deviation of the sampling distribution of x̄?

Answer 15

σ/sqrt(n)

Question 16

If the population has a Normal distribution, then what is the shape of the sampling distribution of x̄?

Answer 16

Normal, regardless of the sample size

Question 17

If the population shape is non-Normal (or we are not told its shape) and there is a small n, what is the shape of the sampling distribution of x̄?

Answer 17

Similar to the shape of the population.

Question 18

If the population shape is non-Normal (or we are not told its shape) and there is a large n with a finite standard deviation, what is the shape of the sampling distribution of x̄?

Answer 18

Approximately Normal

Question 19

What does the Central Limit Theorem state?

Answer 19

As long as n≥30 and there is a finite standard deviation, then the shape of the sampling distribution is approximately Normal.
Also known as the Fundamental Theorem of statistics.

Question 20

Parameter

Answer 20

A number that describes the population.

In statistical practise, the value of a parameter is not known because we cannot examine the entire population.