AP Stats

True of False: The sampling distribution of the sample proportion ˆp describes the distribution of values taken by the sample proportion ˆp in all possible samples of the same size from the same population.

• True

• False

This describes the _____________: Shape: When n is small and p is close to 0, the sampling distribution of pˆ is skewed to the right. When n is small and p is close to 1, the sampling distribution of pˆ is skewed to the left. Finally, the sampling distribution of pˆ becomes more Normal when p is closer to 0.5 or n is larger (or both).

• Shape

• Outliers

• Center

• Variability

This describes _______________: The mean of the sampling distribution of pˆ is equal to the population proportion p. This makes sense because the sample proportion pˆ is an unbiased estimator of p.

• Shape

• Outliers

• Center

• Variability

This describes ________________: The value of σpˆ depends on both n and p. For a specific sample size, the standard deviation σpˆ is larger for values of p close to 0.5 and smaller for values of p close to 0 or 1. For a specific value of p, the standard deviation σpˆ gets smaller as n gets larger. Specifically, multiplying the sample size by 4 cuts the standard deviation in half.

• Shape

• Outliers

• Center

• Variability

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

• A

• B

• C

• D

• E

Is this a probability distribution?

• No

• Yes

The sampling distribution of pˆ is approximately ______ as long as the Large Counts condition is satisfied: np≥ 10 and n(1−p)≥10.

If the large counts condition has been met for ^p1 and ^p2, then ^p1-^p2 is approximately normal.

• True

• False

What is the standard deviation of the sampling distribution if the population standard deviation is 15 and the sample size is 100?

• 1.5

• 0.15

• 15

• 5