AP Stats symbols and formulas

\hat{p}

Sample proportion (observed proportion from your data)

p

True population proportion (unknown value you are estimating)

p_0

Hypothesized population proportion (used in the null hypothesis)

p-value

Probability of getting a result as extreme or more extreme, assuming the null hypothesis is true

z

Z-score; number of standard deviations a sample statistic is from the mean

z^*

Critical z-value for a given confidence level (used in confidence intervals)

-z^*

Negative critical z-value for a given confidence level (symmetric with z^*)

H_0

Null hypothesis; the default assumption that there is no difference or effect

H_a

Alternative hypothesis; the claim you're testing for, suggesting a difference or effect

n

Sample size (number of individuals in the sample)

N

Population size (number of individuals in the entire population)

n\hat{p}

Expected number of successes in the sample based on the sample proportion

n\hat{q}

Expected number of failures in the sample based on the sample proportion (where \hat{q} = 1 - \hat{p})

np_0

Expected number of successes based on the null hypothesis proportion

nq_0

Expected number of failures based on the null hypothesis proportion (where q0 = 1 - p0)

\sqrt{ \frac{ \hat{p}\hat{q} }{n} }

Standard error of the sample proportion (used in confidence intervals)

\sqrt{ \frac{ p0q0 }{n} }

Standard deviation of the sampling distribution under the null hypothesis

z^* \cdot \sqrt{ \frac{ \hat{p}\hat{q} }{n} }

Margin of error for a confidence interval for a population proportion

\hat{p} \pm z^* \cdot \sqrt{ \frac{ \hat{p}\hat{q} }{n} }

Confidence interval formula for estimating a population proportion

\left( \frac{ \hat{p} - p_0 }{ \sqrt{ \frac{ p_0(1 - p_0) }{n} } } \right)

Z-test statistic for a significance test of a proportion