Sampling Distributions

Question 1

Sampling Distributions

Answer 1

The probability distrbution of a sampling statistic.

Different Distributions based on:

• Sample Size (n)
• Statistic
• Sampling Design

The statistic you get for the sample depends on the sample you take

Question 2

Sampling distributions can be characterized by their

Answer 2

Shape, Center and Spread.

Specific values depends on the sampling distribution

Relationship between characteristics of sampling distributions and population parameters is known for many statistics and sampling designs.

Standard deviation of sampling distribution can be used to estimate typical sampling error for a statistic

Question 3

When is the sampling distribution normally distributed?

Answer 3

• When the sampling distribution comes from a normally distributed population
• when the sample size is greater than or equal to fifty

Question 4

Central Limit Theorem

Answer 4

If the sample size is large enough, the distribution of sample means can be approximated by a Normal distribution.

Question 5

The sampling distribution of sample proportions

Answer 5

For an SRS of n,

mu = np

sigma = sqrt(p(1-p)/n

Question 6

Quantitative variable: population

Answer 6

Population/Sample Distribution:
when our variable of focus-the variable
being measured-is quantitative, we could potentially use a Normal model to assign
probabilities related to drawing a particular individual from the population.

Question 7

Quantitative Variable Sampling Distribution

Answer 7

we are
interested in assigning probabilities to values of a sample statistic.

, because the sample mean is a continuous random
variable, we could potentially model the sampling distribution of sample means using a
Normal probability model.

Question 8

Categorical Variable: Population

Answer 8

When we think about randomly selecting an individual from the population, and
determining their gender, the value we obtain won’t be a random variable, because the
values are categorical. Instead, if we imagine what the population distribution would
look like in this case, it would simply be a series of labels

• No normal distribution
• No binomial distribution

Question 9

Categorical Variable: Sampling

Answer 9

-Summarize the data of the categorical variable with a count to determine the relative proportions

-The value of the count will be a random
variable, which we could call Y

-Y varies from sample to sample

-Since we are counting the number of individuals that have a particular characteristicthat is, are a ‘success’-in a sample, we might be able to model those counts as a
Binomial distribution, provided the binomial setting applies

-we can also use the sample proportion rather than count for our distribution

Question 10

Summary: Determining Which distribution to use

Answer 10

1) Think about the type of distribution (population;sampling;sample)
2) Type of variable we are working with (categorical or quantitative)
3) if it is the distribution of a random
variable, we can start thinking about what probability model is appropriate for assigning
probabilities to outcomes of the variable.

-note: in the sampling distribution of the sample statistic;
because a statistic is always a number, the sampling distribution of a sample statistic will
always be a distribution of a quantitative variable;