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Title: Elements of Hypothesis Testing
Description: These notes explain how to conduct and analyze a hypothesis test. These are college level notes but they can also be used for high school classes and AP courses.
Description: These notes explain how to conduct and analyze a hypothesis test. These are college level notes but they can also be used for high school classes and AP courses.
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Elements of Hypothesis Testing
Thursday, March 3, 2016
2:04 PM
The Elements of a Test of Hypothesis
• A statistical hypothesis is a statement about the numerical value of a population
parameter
○ Null hypothesis (Ho): represents the hypothesis that will be accepted
unless the data provide convincing evidence that it is false; the "status
quo"
○ Alternative hypothesis (Ha): the hypothesis that will be accepted only if
the data provide convincing evidence of its truth
• The test statistic is a sample statistic computed from the information provided
in the sample that the researcher uses to decide between the null and
alternative hypothesis
○ Zstat if N > 30, Tstat if N < 30
○ Z = (standard deviation - null hypothesis)/(s/sqrt(n))
• A Type I error occurs if the researcher rejects the null hypothesis in favor of the
alternative hypothesis when, in fact, Ho is true
○ ⍺ = P(Type 1 error)
• The rejection region of a statistical test is the set of possible values of the test
statistic for which the researcher will reject Ho in favor of Ha
• A Type II error occurs if the researcher accepts the null hypothesis when, in fact,
Ho is false (denoted by ℬ)
• If the test statistic does not fall into the rejection region, it is better to state the
conclusion as "insufficient evidence to reject Ho"
Elements of a Test of Hypothesis
Null Hypotheses (Ho): the status quo
Alternative Hypothesis (Ha): the truth we will adopt that contradicts the null
Test Statistic: sample statistic used to decide whether to reject the null
Rejection Region: the value of ⍺ chosen as the level of significance
Assumptions: clear statement of any assumptions made about the population
being sampled
Experiment and Calculation of Test Statistic
Conclusion: 1
...
if the test statistic does not fall within the rejection
region, reserve judgment on which hypothesis is true
Formulating Hypotheses and Setting Up the Rejection Region
Experiment and Calculation of Test Statistic
Conclusion: 1
...
if the test statistic does not fall within the rejection
region, reserve judgment on which hypothesis is true
Formulating Hypotheses and Setting Up the Rejection Region
• A test is one sided if the null hypothesis says a parameter is either greater than
or less than a value
• A test is two sided if the null hypothesis says a parameter is either larger or
smaller than a value (does not equal a value)
Title: Elements of Hypothesis Testing
Description: These notes explain how to conduct and analyze a hypothesis test. These are college level notes but they can also be used for high school classes and AP courses.
Description: These notes explain how to conduct and analyze a hypothesis test. These are college level notes but they can also be used for high school classes and AP courses.