STA 3381 Lecture Notes - Lecture 11: Null Hypothesis, Calorie, Test Statistic
23 May 2018
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8.1
● Reject and failed to reject
● Null hypothesis
● No evidence for null, null is only rejected when there is evidence for the alternative
● Null can be thought of what we have now, and question is if the alternative better?
● Alternative, Ha is often referred to as researcher’s hypothesis”
● We function under assumption that the null is exactly equal to the parameter
● The sign in the null will always be “equal to”
● Question on final: can give nulls and alternatives and ask which one is valid.
Test procedures:
● Evidence to reject null value can be that the probability of finding the parameter is
0.01%.
● Reason to not reject is #2 in example:” 25% chance of getting something at least as
congtradictory….” (from slide 20)
● The further you go away from the hypothesized values, the more CONTRADICTORY
○ Form ex. 8.1, is x=37, and if we choose a value of 35, it is more contradictory,
since it is even smaller, since the null was 50.
○ But how small is small enough to reject the null? For the value.
● P value: probability calculated assuming null is true
● Null is rejected if less than or equal to what we define as the level of significance
○ Most common level of signicance is 0.05, 0.01, 0.001, and 0.1
■ 0.05 is the most popular
○ The level of significance is always stated before the test is run. If not, cheating
● The smaller than the level of significance, more protection is given to null hypothesis
● If you have an expensive process, we want a lot of evidence that this process works. We
say that alpha=0.01, which is small.
○ Protecting the fact that we don’t have to spend money unless overwhelming
evidence that this expensive process works.
● The smaller the P-value, the stronger the evidence against Ho and in favor of Ha.
● Court case analogy:
○ Ho (null) is innocence
○Tyoe 1 error is when rejecting Ho when it is true. → convicting an innocent
person
○Type 2 error is when you don’t reject Ho when it is false. → letting a guilty
person go.
Document Summary
No evidence for null, null is only rejected when there is evidence for the alternative. Alternative, ha is often referred to as researcher"s hypothesis . We function under assumption that the null is exactly equal to the parameter. The sign in the null will always be equal to . Question on final: can give nulls and alternatives and ask which one is valid. Evidence to reject null value can be that the probability of finding the parameter is. Reason to not reject is #2 in example: 25% chance of getting something at least as congtradictory . (from slide 20) The further you go away from the hypothesized values, the more contradictory. 8. 1, is x=37, and if we choose a value of 35, it is more contradictory, since it is even smaller, since the null was 50. P value: probability calculated assuming null is true.
