AP Statistics Review

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# AP Statistics Review - PowerPoint PPT Presentation

AP Statistics Review. Inference for Means (C23-C25 BVD ). Unless the standard deviation of a population is known, a normal model is not appropriate for inference about means. Instead, the appropriate model is called a t-distribution .

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### AP Statistics Review

Inference for Means (C23-C25 BVD)

Unless the standard deviation of a population is known, a normal model is not appropriate for inference about means. Instead, the appropriate model is called a t-distribution.
• T-distributions are unimodal and symmetric like Normal models, but they are fatter in the tails. The smaller the sample size, the fatter the tail.
• In the limit as n goes to infinity, the t-distribution goes to normal.
• Degrees of freedom (n-1) are used to specify which t-distribution is used.
• T-table only has t-scores for certain df, and the most common C/alphas. If using table and desired value is not shown, tell what it would be between, or err on the side of caution (choose more conservative df, etc.)
• Use technology to avoid the pitfalls of the table when possible.
T-distributions
X-bar +/- t*df(Sx/sqrt(n))
• Sample statistic +/- ME
• ME = # standard errors reaching out from statistic.
• T-interval on calculator
Confidence Interval for 1 Mean
Draw or imagine a normal model with C% shaded, symmetric about the center.
• What percent is left in the two tails?
• What percentile is the upper or lower fence at?
• Look up that percentile in t-table to read off t(or use invt(.95,df) or whatever percent is appropriate)
Finding the critical value (t star)
ME = t*(SE)

Plug in desired ME (like within 5 inches means ME = 5).

Plug in z* for desired level of confidence (you can’t use t* because you don’t know df).

Plug in standard deviation (from a sample or a believed true value, etc. Solve equation for n.

Finding Sample Size
For inference for means check:
• 1. Random sampling/assignment?
• 2. Sample less than 10% of population?
• 3. Nearly Normal? – sample size is >30 or sketch histogram and say could have come from a Normal population.
• 4. Independent – check if comparing means or working with paired means
• 5. Paired - check if data are paired if you have two lists
Conditions/ Assumptions to Check
Null: µ is hypothesized value
• Alternate: isn’t, is greater, is less than
• Hypothesized Model: centers at µ, has a standard deviation of s/sqrt(n)
• Find t-score of sample value using n-1 for df
• Use table or tcdf to find area of shaded region. (double for two-tail test).
• T-test on calculator– report t, df and p-value.
Hypothesis Test for 1 mean
If data are paired, subtract higher list – lower list to create a new list, then do t-test/t-interval.
• If data are not paired:
• Check Nearly Normal for both groups – both must individually be over 30 or you have to sketch each group’s histogram and say could’ve come from normal population
• CI: mean1-mean2 +/- ME --- use calculator because finding df (and therefore also t*) is rather complicated.
• SE for unpaired means is sqrt(s12/n1 + s22/n2)
• If calculator asks “pooled” – choose “No”.
• Null for paired: µd = 0 (usually)
• Null for unpaired: µ1 - µ2 = 0
• Don’t forget to define variables.
• Use 2-Sample T-Test and 2-Sample T-Interval in calculator for data that are not paired.
Inference for 2 Means
State: name of test, hypothesis if a test, alpha level if a test, define variables
• Plan: check all conditions – check marks and “yes” not good enough
• Do: interval for intervals, test statistic, df (if appropriate) and p-value for tests It is good to write the sample difference if doing inference for two proportions or two means, but make sure no undefined variables are used
• Conclude: Interpret Confidence Interval or Hypothesis Test – See last slide show for what to say
What to Write