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Quiz 2
91.5.22
1. (30%)
A sample of 36 observations is taken. The sample mean is 83.96 and the sample
standard deviation is 12. Then, for the hypothesis
H 0 :   87 v.s. H a :   87 ,
(a) using   0.05 , test the hypothesis based on the classical hypothesis test?
(b) using   0.15 , test the hypothesis based on p-value?
(c) using   0.1, test the hypothesis based on the confidence interval approach?
2. (20%)
Consider the following hypothesis test,
H 0 : p  0.5 v.s. H a : p  0.5 .
A sample of 200 provided a sample proportion p  0.57 .
(a) using   0.05 , test the hypothesis based on the classical hypothesis test?
(b) using   0.1, test the hypothesis based on p-value?
3. (30%)
A sample of 6 observations, 18, 20, 16, 19, 17, 18, is taken. Suppose the
population is normally distributed. Then,
(a) for the hypothesis,
H 0 :   20 v.s. H a :   20 ,
using   0.05 , test the hypothesis based on the classical hypothesis test?
(b) for the hypothesis,
H 0 :   18 v.s. H a :   18
using   0.05 , test the hypothesis based on p-value?
(c) for the hypothesis,
H 0 :   17 v.s. H a :   17
using   0.05 , test the hypothesis based on the confidence interval approach?
4. (20%)
(a) Let X be Poisson random variable with mean 
1
(i.e., f (i ) 
 i e u
i!
, i  0, 1, 2, 3, ) .
For the following hypothesis test
H 0 :   2 vs H a :   2 ,
we reject
H0
as
X  0 or 3 . Please calculate
  the probabilit y of making a type I error .
(b) Consider the following hypothesis test,
H 0 : p  0.75 v.s. H a : p  0.75 .
A sample of 300 is selected. Test the hypothesis based on p-value as

p  0.68

p  0.77 .
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