1 / 9

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 .

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about ' AP Statistics Review' - hanley

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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* normal model is not appropriate for inference about means. Instead, the appropriate model is called a df(Sx/sqrt(n))

• Sample statistic +/- ME

• ME = # standard errors reaching out from statistic.

• T-interval on calculator

Confidence Interval for 1 Mean

Finding the critical value (t star)

• ME = t*(SE) about the center.

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: about the center.

• 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 about the center.

• 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