e null hypotheses against the alternative. D Question 13 2 pts Suppose the milit

Question

e null hypotheses against the alternative. D Question 13 2 pts Suppose the military has designed a new missile-guidance system. With the old system, 80% of missiles landed within thirty meters of the target at a range of five hundred miles. The military claims that the new system is better (that more than 80% of missiles will land within thirty meters at five hundred miles). Ten randomly-chosen, identical missiles will be launched using the new guidance system in order to test the null hypothesis that the accuracy rate of the new system is no better than that of the old system against the alternative hypothesis that the accuracy rate of the new system is better

Explanation / Answer

Question 15

Sol: Option d) 11

The minimum sample size is n that permits the maximum probability of Type I error to be controlled at 10%.
so that means at least we have one value such that we can have a rejection region.

Pr(X >= C ; n ; 0.8) <= 0.10
0.8n < 0.10
n ln (0.8) < ln (0.10)
n < 10.32 ? 11
so n shall be minimum 11 to have atleast one value of C where we can have a rejection region.

Question 16

Sol:

The military decides to increase the sample size to fifteen. What critical value should be used to control the maximum probability of Type I error at 10%

Option d) 15

Given Sample size = 15
Now type I error = 10%
so let say critical value c above which we shall reject the null hypothesis,
Pr(X >= C ; 15 ; 0.8) <= 0.10
so BIN (X < C ; 15 ; 0.8) > = 0.90
Binomial table the value of C = 15
that means that if 15 out of 15 is successful here then we reject the null hypothesis.

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