6.2 Large Sample Significance Tests for a Mean. “The reason students have trouble understanding hypothesis testing may be that they are trying to think.” Deming. In a law case, there are 2 possibilities for the truth—innocent or guilty
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“The reason students have trouble understanding hypothesis testing may be that they are trying to think.” Deming
Held on to unless there is sufficient evidence to the contrary
We reject H0 in favor of Haif there is enough evidence favoring Ha
1. About parameter(s): means or variances
2. About the type of populations: normal ,
binomial, or …
This is the same as to ask if p=0.5
The assertion is μ=1000
Notation: H0: p=0.5 and H0:μ=1000
If we reject the above null hypotheses,
the appropriate conclusions we arrive are
called alternative hypotheses
Ha: p0.5 Ha: μ1000
or may be
=P(type I error)
=P(reject H0 when H0 true)
(a small number)
=P(type II error)
=P(accept H0 when H0 false)
A random sample of size n=10 is taken,
and sample mean is calculated
If the p-value is small,
This type of data are unlikely if H0 is true.
The fact that we are looking at this data set right now indicates that H0 is likely not true.
The null hypothesis looks bad reject H0 .
Given that n=25, s=100, and sample mean is 1050,
1. Test the hypotheses H0: m=1000 vs HA: m<1000 at level a=0.05.
2. Test the hypotheses H0: m=1000 vs HA: m≠1000 at level a=0.05.
More evidence against H0 is smaller values of z
Evidence against H0 is z values away from 0 in either direction