7.2 Sampling Distributions Conditions and Calculations

Question 1

Why do we check the random condition?

Answer 1

To make sure the sample isn’t biased and therefore the sampling distribution will be centered at the true parameter

Question 2

Why do we check for Independence (10% condition)?

Answer 2

So that we can use the standard deviation formula(s) on the formula sheet. These formulas are based on binomial calculations which require each “trial” to be independent.

Question 3

How do we check for Independence?

Answer 3

Is sampling without replacement (most common), assume that our sample size (n) is less than 10% of the whole population (in context). If the scenario is more of an experiment that doesn’t really have a set population, you can just state that each trial is independent of the others.

Question 4

Why does the 10% condition establish independence?

Answer 4

When sampling without replacement, the probabilities for each “person” will change but as long as you don’t take too many (10%), the probabilities don’t change too much, so it’s okay.

Question 5

Why do we need to check large counts?

Answer 5

The larger the sample size, the more the sampling distribution will look normal. So, if we use normalcdf to analyze the problem, it won’t be accurate if our sample is too small.

Question 6

How do we check large counts?

Answer 6

For proportions: np and n(1-p) are both at least 10. For means: n>=30 OR the population is known to be approx normal itself.

Question 7

How do we use sampling distributions to answer probability questions?

Answer 7

Whenever asked for the probability that the mean or proportion of a sample is greater (or less) than something, you’ll use a normal curve with mean and s.d. from the formula sheet.

Question 8

How do you know the shape of a sampling distribution?

Answer 8

Usually “approximately normal” because you check the appropriate large count condition. If large counts is not met, then just the shape is unknown.