OLI Statistics Exam 3

Instructions

Copy these formulas for use as you take the exam.

The Standard Deviation (SD) equation is = $LaTeX: \sqrt{\frac{p\left(1-p\right)}{n}}$

Z = $LaTeX: \frac{Statistic\:-\:Parameter}{S\tan dard\:Error\:\left(SD\right)}$ $LaTeX: =\frac{phat\:-p}{SD}$

Test Statistics

Z = ˆ p - p

_$0$

\frac{{/[(}}{\sqrt{p_{0} (1 - p_{0}))/ n]}}

The confidence interval is sample proportion ± margin of error.

For a 95% confidence interval the margin of error is two standard errors.

sample proportion ± margin of error = sample proportion ± 2 SE

95% Confidence Interval = $LaTeX: phat\:\pm2\sqrt{\frac{phat\left(1-phat\right)}{n}}$

\begin{matrix} Sample proportion \pm margin of error = ˆ p \pm Z c[\sqrt{\frac{ˆ p (1 - ˆ p)}{n]}} \end{matrix}

For our most common confidence levels, the values of Z_c are:

90% confidence interval: Z_c≈ 1.645
95% confidence interval: Z_c≈ 1.960 (2 is a rough approximation; 1.960 is more accurate)
99% confidence interval: Z_c≈ 2.576

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