AP Stats Unit 5

Statistic

Number that describes some characteristic of a sample.

Parameter

A number that describes some characteristic of the population.

x̄ (the sample mean) estimates…

μ (the population mean)

p̂ (the sample proportion) estimates…

p (the population proportion)

s_x (the sample standard deviation) estimates…

σ (the population standard deviation

When defining a parameter, use the words

all or true

Sampling variability

refers to the fact that different random samples of the same size from the same population produce different values for a statistic.

Sampling distribution

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

Approximate sampling distribution

taking many samples, calculating the value of the statistic for each sample, and graphing the result

Population distribution

gives the values of the variable for all individuals in the population.

Distribution of sample data

shows the values of the variable for the individuals in a sample.

sampling distribution of the sample proportion

displays the values of p̂ from all possible samples of the same size.

unbiased estimator

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

Estimator with high bias and low variability

Estimator with low bias and high variability

Estimator with high bias and high variability

Estimator with no bias and low variability

Precise

Repeated samples give similar results.

Accurate

Our sample statistics center on the population parameter.

Variability

the spread of its sampling distribution. Larger samples give less variability.

Unbiased estimator

if the center (mean) of its sampling distribution is equal to the true value of the parameter.

Sampling distribution of the sample proportion

describes the distribution of values taken by the sample proportion p̂ in all possible samples of the same size from the same population.

When n is small and p is close to 0

the sampling distribution of p̂ is skewed to the right

When n is small and p is close to 1

the sampling distribution of p̂ is skewed to the left.

When p is closer to 0.5 or n is larger

the sampling distribution of p̂ becomes more Normal

The mean of the sampling distribution of p̂ is equal to

the population proportion p

the standard deviation 𝜎_p̂ is larger for values of p

close to 0.5 and smaller for values of p close to 0 or 1

the standard deviation 𝜎_p̂ is smaller

as n gets larger

Multiplying the sample size by 4

cuts the standard deviation in half

10% condition

n < 0.10N

Large Counts Condition

np ≥ 10 and n(1-p) ≥ 10

When the large counts condition is satisfied

The sampling distribution of p̂ is approximately Normal

Mean of the sampling distribution of p̂

u_p̂ = p

Standard deviation of p̂

σ_{p̂ =} √p(1-p)/n

The mean of the sampling distribution of x̄

μ_x̄ = μ

The standard deviation of the sampling distribution of