$go to Math$

AP Statistics Unit 5: Sampling Distributions

Ch 7: Sampling Distributions

Studied by 12 people

1.0(1)

Get a hint

Hint

x bar (the sample mean)

1 / 22

Earn XP

Description and Tags

Statistics

Sampling Distributions

AP Statistics

Unit 5: Sampling Distributions

23 Terms

x bar (the sample mean)

estimates μ (the population mean)

New cards

p hat (the sample proportion)

estimates p (the population proportion)

New cards

Sx (the sample st. dev.)

estimates σ (the population st. dev.

New cards

statistic

describes characteristics of a sample

New cards

parameter

describes characteristics of a population

New cards

sampling variability

different random samples of the same size from the same population product different values for a statistic

New cards

sampling distribution

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

New cards

unbiased estimator

mean of the sampling distribution is equal to the value of the parameter being estimated

New cards

variability

described by the spread of its sampling distribution — inversely proportional to sample size

New cards

sampling distribution of the sample proportion p hat

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

New cards

mean of the sampling distribution

$<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="\mu_{\hat{p}}=p"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo stretchy="false">^</mo></mover></mrow></mrow></msub><mo>=</mo><mi>p</mi></math>$

New cards

standard deviation of the sampling distribution (as long as the 10% condition is satisfied)

$<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="\sigma_{\hat{p}}=\sqrt{\frac{p\left(1-p\right)}{n}}"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo stretchy="false">^</mo></mover></mrow></mrow></msub><mo>=</mo><msqrt><mfrac><mrow><mi>p</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>−</mo><mi>p</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mi>n</mi></mfrac></msqrt></math>$

New cards

sampling distribution is approximately Normal if

the Large Counts condition is satisfied

New cards

mean of the sampling distribution of p1-p2

$<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="\mu_{\hat{p}_1-\hat{p}_2\ =\ p_1-p_2}"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><msub><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo stretchy="false">^</mo></mover></mrow><mn>1</mn></msub><mo>−</mo><msub><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo stretchy="false">^</mo></mover></mrow><mn>2</mn></msub><mtext></mtext><mo>=</mo><mtext></mtext><msub><mi>p</mi><mn>1</mn></msub><mo>−</mo><msub><mi>p</mi><mn>2</mn></msub></mrow></msub></math>$

New cards

standard deviation of p1-p2 if the 10% condition is met

New cards

shape of the sampling distribution of p1-p2 is approximately Normal if

the Large Counts condition is met for BOTH samples

New cards

sampling distribution of the sample mean x-bar

distribution of values taken by the sample mean x-bar in all possible samples of the same size from the same population

New cards

mean of the sampling distribution of x-bar

$<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="\mu_{\overline{x}}=\mu"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo accent="true">―</mo></mover></mrow></msub><mo>=</mo><mi>μ</mi></math>$

New cards

standard deviation of the sampling distribution of x-bar as long as the 10% condition is met

$<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="\sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo accent="true">―</mo></mover></mrow></msub><mo>=</mo><mfrac><mi>σ</mi><msqrt><mi>n</mi></msqrt></mfrac></math>$