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Unformatted text preview: is: Holds the claim to be challenged, to be refuted if possible. H0 : µ ≥ 60.
Alternative Hypothesis: Alternative theory to be maintained if the null hypothesis is
rejected: H1 (HA ) : µ < 60.
As a researcher if I think that the average yearly income at 30 for university graduates (µ) is less
than 60 thousand dollars a year, to back up my claim, I challange the opposite claim, that it is
higher than 60. If I reject the H0 , then I get evidence for my theory.
Alternatively, you might also be asked a hypothesis directly. “Test the claim that µ is less 50”.
Then this claim should be put in the null hypothesis. Utku Suleymanoglu (UMich) Hypothesis Testing 4 / 39 Null and Alternative Hypotheses Examples 1. You are unhappy with your car: you think your new car travels less than 30 mpg. To get it
serviced for free, you want to ﬁnd evidence that MPG < 30. You record your consumption
for a month and build a sample. You challange the claim that E (MPG ) = µ ≥ 30
H0 :µ ≥ 30
H1 :µ < 30
2. You are an engineer and have a machine in your factory that produces pencils. You think the
machine is broken, and it produces pencils of incorrect lenghts. It supposed to produce
pencils of an average length of 5 inches. You collect a sample and test:
H0 :µ = 5
H 1 :µ = 5
KEY: In all hypothesis testing, you look at the evidence and decide whether you have enough
evidence to reject the null hypothesis. If you don’t have it, you fail to reject the null hypothesis:
you don’t accept the null hypothesis. Jury analogy. . . Utku Suleymanoglu (UMich) Hypothesis Testing 5 / 39 Null and Alternative Hypotheses Type I and II Errors The hypothesis testing we will do is not perfect: there could be mistakes.
Testing Result H0 is True H0 is False Reject H0 Type I Error Correct Fail to Reject H0 Correct Type II Error TYPE I Error: Null Hypothesis is true and you reject it. Probability = α. Signiﬁcance level. We
can choose this.
TYPE II Error: Null Hypothesis is false and you...
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- Spring '08