Statistics for Decision- Making in Business - Maricopa Community ...

2) Decision Rule: We will reject the null hypothesis when the likelihood of
observing something as small/large or smaller/larger than 16 out of 1000
bushels is no larger than a 1% probability, under the assumption of the null
hypothesis. That is,
( )
3) We will reject if the observed value of is smaller or larger than some
cutoff values of . That is, if it is smaller than some value, say , or larger than
some value, say , then we will reject . Remember, we set-up a hypothesis
first, then do the test. Even though 16 is larger than 15 out of 1000, we did not
know this to begin with. We are still testing whether or not this value is
significantly different and do not care about the direction of the difference.
4) Based on the sample evidence, we will either:
a) Reject in favor of of machines fail. That is, either a
significantly fewer number of them fail, or a significantly greater number
of them fail.
b) Fail to reject . We do not have sufficient evidence to conclude that new
machines fail more or less when compared to the old machine.
10.
1) Type I: We conclude the farmer‟s method reduces crop destruction, when there is
no difference; Type II: We conclude the farmer‟s method is no different than the
old method, when in fact there is less than 7% crop destruction with his new
method.
2) Type I: We conclude the instructors students perform better than his former
students, when in fact there is no difference; Type II: We conclude that his new
students perform just as well as his former students, when in fact they do better.
3) Type I: We conclude that the new machines fail more or less than the former
machines, when in fact there is no difference; Type II: We conclude that there is
no difference between the failure rates of the new and old machines, when in fact
there is a significant difference.
11. Increasing means we will reject less often, as we set more stringent conditions upon
the rejection process. If we reject less often, then there is an elevated likelihood that we
may fail to reject, when in fact we should. This is precisely what a Type II error is.
Statistics for Decision-Making in Business © Milos Podmanik Page 246