Solution:
(a) Explain type 1 error in the context of this problem:
Type I error happens when a null hypothesis is true and we reject it. The probability of type I error is a . In the given question we reject the null hypothesis based on the previously mentioned plot.
(b) We have to find the value of α associated with this test?Is this a good,sensible test?
In the previously mentioned question the null hypothesis is dismissed when
Case 1: Both the randomly selected ledgers are error free
Case 2: When in any event one of them is without mistake and we
draw a third record and it is found to be error free. In the Case
1, the likelihood of a record being error free is 0.5
The likelihood that both the ledgers are error free is 0.25
The Case 2 can be separated into two sections
(1) When both the ledgers drawn are mistaken
For this situation the likelihood of dismissing the null hypothesis is 0.125
(2) At the point when one of the two drawn register is error blunder.
For this situation the likelihood of rejecting null hypothesis is 0.125
The likelihood of committing the type 1 error is 0.25+0.125+0.125 = 0.50
So the estimation of is 0.5.
The test can't be considered a a reasonable one since it has no measurable basis.
(c) Explain your answer based on the rejection rule(i.e. region) and the hypotheses.
The district of rejection has no statistical basis. The hypothesis is rejected based on the irregular drawing of records . The test measurement doesn't keep any standard appropriation and can't be viewed as a reasonable one.
(d) Explain type 2 error in the context of this problem
The type 2 error is committeed when the alternative hypothesis is accepted even when it is false
the probability of type 2 error is
= 1 -
= 0.50
(e) We calculate (P0) = P(Type II error| p = p0) as a function of p0.What would be (0.7)
here
The acceptance of alternate hypothesis even when it is wrong implies that p = 0.05
= p/10
(0.7) = 0.07
Therefore,
(0.7) = 0.07
.
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