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6. This is the probability that we reject the null hypothesis when it is, in fact, true. That is
( ) . This allows us to be 95% confident that we fail to reject
when it is true, a correct decision.
7.
1) Hypotheses:
8.
2) Decision Rule: We will reject the null hypothesis when the likelihood of
observing something as small or smaller than 52 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 than some cutoff
value of .
4) Based on the sample evidence, we will either:
a. Reject in favor of of insect-related crop destruction for the
farmer‟s new method.
b. Fail to reject . We do not have sufficient evidence to conclude that the
farmer‟s new method is better than his old method.
1) Hypotheses:
2) Decision Rule: We will reject the null hypothesis when the likelihood of
observing something as large or larger than ̅ is no larger than a 5%
probability, under the assumption of the null hypothesis. That is,
( ̅ )
̅ 3) We will reject if the observed average of is larger than some cutoff
value of ̅.
4) Based on the sample evidence, we will either:
a. Reject in favor of out of 5 questions are answered correctly by
his students (as of recent observations).
b. Fail to reject . We do not have sufficient evidence to conclude that the
instructor‟s more recent students do better on the AP exam than his former
students.
9.
1) Hypotheses:
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