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STA 1020
Hypothesis Testing Cheat Sheet Recall that hypothesis testing is a procedure that enables us to choose between two hypotheses when we are uncertain about our measurements (i.e. statistics). Here we try to have a uniform standard for evaluating claims on population parameters. Steps to Hypothesis Testing:
- Establish the null hypothesis.
- Establish the alternate hypothesis (called the research hypothesis).
- Calculate the P-value.
- State the conclusion. Make sure to put in the context of the problem. Error Types: Test #1: Proportions Hypotheses Test Statistic Critical Value When To Reject ๐ฏ๐? Other notes Involves โpโ, not ๐. Equality is always with null hypothesis.
Given as a value of ๐ผ When Test statistic is less than significance level โ For alternative hypothesis: One-sided Test: ๐ < 0. 2 ๐ > 0. 4 Two-sided Test: ๐ โ 0. 3 Test #2: Means Hypotheses Test Statistic Critical Value When To Reject ๐ฏ๐? Other notes Involves โ๐โ, not ๐ฅ. Equality is always with null hypothesis.
Given as a value of ๐ผ When Test statistic is less than significance level โ For alternative hypothesis: One-sided Test: ๐ < 2 ๐ > 4. 2 Two-sided Test: ๐ โ 32. 1
Test #3: Chi-Square Test for Goodness of Fit Hypotheses Test Statistic Critical Value When To Reject ๐ฏ๐? Other notes Two cases for ๐ป 9 :
- Probabilities are all the same.
- Probabilities are different. Alternate Hypothesis is always โThere is some difference amongst the probabilities. (in terms of expected prob).
๐;^ =
<=>?= @ ?= Observed Count: ๐B Expected Count: ๐ธB = ๐๐B Need Degrees of Freedom: df = k โ where k is the number of possible outcomes for each trial. Also need significance level ๐ผ.
- If ๐;-statistic < ๐;-critical value, then accept ๐ปD
- If ๐;-statistic > ๐;-critical value, then reject ๐ปD It may be necessary to calculate the expected count for each different probability in case #2 of the hypotheses. Test #4: Chi-Square Test for Association Hypotheses Test Statistic Critical Value When To Reject ๐ฏ๐? ๐ป 9 : The two variables in the population are independent (no association) ๐ปF: The two variables in the population are not independent (associated)
๐;^ =
<=>?= @ ?= Observed Count: ๐B ๐ธ๐ฅ๐๐๐๐ก๐๐ ๐ถ๐๐ข๐๐ก: ๐ธB =
๐๐๐ค ๐ก๐๐ก๐๐ ร ๐๐๐๐ข๐๐ ๐ก๐๐ก๐๐
Need Degrees of Freedom: df = ( r โ 1)( c โ 1), r is # of rows, & c is # of columns. Also need significance level ๐ผ.
- If ๐;-statistic < ๐;-critical value, then accept ๐ปD
- If ๐;-statistic > ๐;-critical value, then reject ๐ปD Test #5: Two Population Means Hypotheses Test Statistic Critical Value When To Reject ๐ฏ๐? Other notes Involves โ๐โ, not ๐ฅ. Equality is always with null hypothesis. Two ways: ๐ป 9 : ๐V โ ๐; โฅ 0 ๐ปF: ๐V โ ๐; < 0
- or- ๐ป 9 : ๐V โฅ ๐; ๐ปF: ๐V < ๐;
๐ฅV โ ๐ฅ; โ ๐V โ ๐;
๐V^ ;
๐V
๐;^ ;
Given as a value of ๐ผ When Test statistic is less than significance level โ For alternative hypothesis: One-sided Test: ๐V โ ๐; < 0 ๐V โ ๐; > 0 Two-sided Test: ๐V โ ๐; โ 0
