Question

Let ?1, ?2, … , ?? denote a random sample from a normal population distribution with a known value of ?.

(a) For testing the hypotheses ?0: ? = ?0 versus ??: ? > ?0 where ?0 is a fixed number, show that the test with test statistic ?̅ and rejection region ?̅≥ ?0 + 2.33(?⁄√?) has a significance level 0.01.

(b) Suppose the procedure of part (a) is used to test ?0: ? ≤ ?0 versus ??: ? > ?0 . If ?0 = 100, ? = 25 and ? = 5,

(1) What is the probability of committing a type I error when ? = 99?

(2) What is the probability of committing a type I error when ? = 98?

(3) In general, what can be said about the probability of a type I error when the actual value of ? is less than ?0 ?

Answer #1

Let X1, X2, . . . , X12 denote a random sample of size 12 from
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defined by
(12∑i=1) Xi, ≤2
is a best critical region for testing H0 :θ=1/2 against H1
:θ=1/3.
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A consumer research group is interested in testing an automobile
manufacturer's claim that a new economy model will travel at least
26 miles per gallon of gasoline (H
0: 26).
With a .02 level of significance and a sample of 30 cars, what
is the rejection rule based on the value of for the test
to determine whether the manufacturer's claim should be rejected
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Using a random sample of size 77 from a normal population with
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A consumer research group is interested in testing an automobile
manufacturer's claim that a new economy model will travel at least
27 miles per gallon of gasoline (H
0: 27).
a. With a .02 level of significance and a sample of 40 cars,
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