Unit 3 Formula Sheet



Central Limit Theorem:

(\(n\geq30\) or population is normally distributed)



Mean of the Sampling Distribution: \(\mu_x=\mu\)

Standard Deviation of the Sampling Distribution (Standard Error):

\(\sigma_x=\frac\sigma{\sqrt n}\)

z-Score \(=\frac{{\displaystyle\overset\_x}-\mu_x}{\sigma_x}=\frac{\displaystyle\overset\_x-\mu}{ \frac {\sigma}{\sqrt n}}\)



Population Proportion:

\(\widehat p=\frac xn\)



Unit 3 StatCrunch Instructions


Find the Margin of Error:

Proportion: \(E=\hat{p}- \)lower limit of confidence interval

Mean: \(E=\bar{x}- \)lower limit of confidence interval

Percentiles:

  • Stat
  • Calculators
  • Normal
  • Enter Mean & SD
  • Percentile goes in box AFTER=
  • Sign is always \(\leq\)

Finding Normal Probability

  • Stat
  • Calculators
  • Normal
  • Enter Mean & SD
  • Determine sign \(\leq\) or \(\geq\)
  • Enter number
  • Compute (Probability is # after the =)

Finding Probability: Central Limit Theorem

  • Stat
  • Calculators
  • Normal
  • Enter Mean
  • Enter SD: SD=SD/sqrt(n)
  • Determine sign (≤ or ≥) and enter number
  • Compute (Probability is number after =)

Sample Size: Proportion

  • Stat
  • Proportion Stats
  • One Sample
  • Width Sample Size
  • Put in Confidence Level as a decimal
  • Put in Target % given in the problem as a decimal (use 50% if not given)
  • Width: DOUBLE the margin of error and put in as a decimal
  • Compute

Finding Critical Values: Proportion

  • Stat
  • Calculators
  • Normal
  • Between
  • = confidence level as a decimal
  • 2 z values will be the same. Use the positive one.

Finding Critical Values: Mean

  • Stat
  • Calculators
  • T
  • Between
  • Degrees of freedom (d.f.)= n - 1
  • = confidence level as a decimal
  • 2 T values will be the same. Use the positive one.

Confidence Intervals: Proportion

  • Stat
  • Proportion Stats
  • One Sample
  • Either with data or with summary
  • If given summary-put in number of success and total number
  • Click Confidence Interval Button
  • Put in Level of Confidence
  • Click Show critical value box
  • Compute

Confidence Intervals: Mean

  • Stat
  • T Stats
  • One Sample
  • Either with data or with summary
  • If given summary-put in mean, SD, and sample size
  • Click Confidence Interval Button
  • Put in Level of Confidence
  • Click Show critical value box
  • Compute