Download Confidence Intervals and Hypothesis Testing for Means and

Confidence Intervals and Hypothesis Testing for Means and Proportions
Margin of error (for
confidence intervals)
Proportions
√
Two proportions
√
Confidence
Interval
endpoints
̂
̂̂
̂ ̂
Test statistic (for hypothesis tests)
̂
√
̂
̂
̂
̂ ̂
̂
√ ̂̂(
̅
̅
Single Mean
)
√
√
̅
Two Means
(Independent
samples)
̅
̅
̅
√
√
̅
̅
Two Means
(Matched pairs)
√
√
Goodness of fit
N/A
N/A
Independence or
Homogeneity
N/A
N/A
Correlation
(confidence
interval/test for the
slope)











∑
∑
(
)
(
)
( )
(use software)
( )
(use software)
is the population proportion and
– .
̂ is the sample proportion, and ̂
̂.
For comparing two proportions, and are the population proportions for the two samples, and ̂ and ̂ are
the corresponding sample proportions. ̂ and ̂ are the pooled sample proportions (the sample data from both
groups are pooled together to form them).
is the population mean
̅ is the sample mean
is the sample standard deviation
For independent samples: ̅ and ̅ are the means of two groups, and are the corresponding standard
deviations, and
and
are the corresponding sample sizes.
For paired data: ̅ is the mean difference of the pairs of sample data, is the standard deviation.
and are critical values, and depend on the confidence level.
also depends on df.
is the slope of the regression equation for the sample, is the slope of the regression line for the population.
( ) is the standard error of the slope (use computer software to get).