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      MAT123 Spring 2025 Notes


Wed, 4/16, 8.1
9.1 Null and Alternative Hypotheses
a) Define null and alternative hypotheses for mean and proportion
9.2 Outcomes and the Type I and Type II Errors
a) Define Type I and Type II error and their meaning in the context of applied problems
Watch in
"All of Statistics I in 2.5 Hours" video the part on"Hypothesis Testing" starting at (hours:minutes:seconds) 1:58:17
Read the matching page
hypothesis testing in Stat I in 2 Hours
Watch the Hypothesis Tests pdf file video
Perhaps review
notes from Monday, 4/14 on confidence intervals or
"Brief Summary of A Confidence Interval"
Read Hypothesis Testing
Read "Hypothesis Tests"
Play with
Hypothesis.Tests.2022.xls -- hypothesis testing spread sheet
Check out/write your own hypothesis test
using the TI calculator sample below.

    A hypothesis test is a procedure by which a hypothesis (or statement) which one believes to be true is tested statistically against another hypothesis already in use.


 
    Old Symbols:
  • population mean, (mu),
  • population standard deviation, (sigma),
  • z, the standard normal variable
  • (alpha) - the area under the density function which is not in the confidence interval.
        Sometimes alpha is in the two tails and other times alpha is only in one tail.
    New Symbols:
  • k-- constant, like 70, ex. = 70
  • hypothesis (no symbol) -- a theory or statement which may or may not be true
  • H0 -- read as "H 0" -- the null (original or beginning) hypothesis
  • H1 -- read as "H 1" -- the alternate (new) hypothesis

omnicalculator.com/statistics/critical-value


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