Unit 7: Sampling Distributions

Question 1

Parameter

Answer 1

A number that describes a population, usually what you are looking for in a population. This number is usually unknown.

Question 2

Statistic

Answer 2

A number that describes the sample. Essentially the parameter that is found via the sample.

Question 3

Sampling Variability

Answer 3

The idea that the value of a sample statistic varies in repeated random sampling.

Question 4

Sampling Distribution

Answer 4

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

Question 5

Population Distribution

Answer 5

Gives the values of the variable for all the individuals in the population (Ex: Height of all 300 girls in a school).

Question 6

Distribution of a Sample

Answer 6

Gives the values of the variable for all the individuals in an individual sample (Ex: Height of 20 random girls from the 300).

Question 7

Sampling Distribution

Answer 7

Describes how a sample statistic varies in many samples from a population (Ex: How the average height of many random 20 girls varies between each sample).

Question 8

Unbiased Estimator

Answer 8

A statistic used to estimate a parameter if the mean of its sampling distribution us equal to the true value of the parameter being estimated.

Question 9

Are Unbiased Estimators Perfect?

Answer 9

No; it’s called unbiased because the estimates of repeated samples won’t consistently be too high or too low.

Question 10

Variability of a Statistic

Answer 10

Described by the spread of its sampling distribution.

Question 11

How to determine the Variability of a Statistic?

Answer 11

The size of the random sample.

Question 12

Low Bias

Answer 12

The statistic being slightly off from the parameter but simultaneously staying close to it in value.

Question 13

How do Sampling Distribution and Population Distribution affect Standard Deviation?

Answer 13

A larger Sampling Dist. would result in a smaller Standard Dev., while Population Dist. does not affect the Standard Dev. at all.

Question 14

Distribution of Sample Data vs. Sampling Distribution

Answer 14

Dist. of Sample Data is the distribution of values from one sample, while Sampling Dist. is the distribution of values from many different samples.

Question 15

What Determines the 10% Condition?

Answer 15

The population is at least 10 times larger than the sample size (n<= 0.1(n))

Question 16

What Determines the Normal Condition?

Answer 16

The Sampling Distribution of a Sample Proportion is approx. normal as long as:
np >= 10 AND n(1-p)>=10.

Question 17

What Determines the Central Limit Theorem?

Answer 17

If n>=30.