A Summary

(75% of the Statistics Course on One Page)

Part I: Predicting what will happen to a sample when we know the process.

The Three Step Method Used in the Textbook

1) Figure out the Box

a) What are the tickets?
b) What is the average of the box?
c) What is the standard deviation of the box?

2) Predict the Sum

a) What is the expected value of the sum?
b) What is the standard error of the sum?
{c) To find what will happen to percentage or mean, divide the answers from parts a and b by the sample size.}

OR:

2) Predict the sample mean (or percentage, which is a special mean.)

a) Expected value of sample mean is the average of the box. 1b
b) Standard error of the mean is standard deviation of the box divided by square root of sample size.
{c) To find what will happen to sum, multiply answers a and b by the sample size.}

3) Compute Probabilities

a) Draw the Picture to see what you are looking for.
b) Compute the z-score using the normal curve
c) Use the tables to find the area; make whatever adjustments are necessary.

Part II: Trying to infer the something about the process when we have the sample.

Statistical inference—either confidence intervals or hypothesis testing. Both try to infer what is in the box (population) when have only information from a sample (drawings from the box).

Steps in deriving a confidence interval.

1. Draw the sample, compute the sample mean and standard deviation. (A percentage is a special sort of mean.)
2. Use the mean of the sample to estimate the mean of the population.
3. Use the standard deviation of the sample to estimate the standard deviation of the population. (Textbook's bootstrap.)
4. Use the estimate of the standard deviation of the population to compute an estimated standard error of the mean (or sum or percentage).
5. Decide how confident we want to be in the estimate. You cannot be 100% confident—it must be less. Use this confidence as an area on the normal curve and find a z-score.
6. Your confidence interval is:

Sample average plus or minus z-score times standard error of the mean.

(We will alter 5 eventually and use the t-tables instead. It corrects for the error we introduce when we estimate the standard deviation of the population from the standard deviation of the sample. As the sample gets bigger, the error should get less, and the t-table gets increasingly close to the normal curve.)

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