5) A long-range missile missed its target by average of 0.88 miles. A new steeri
ID: 3157644 • Letter: 5
Question
5)
A long-range missile missed its target by average of 0.88 miles. A new steering device is supposed to increase accuracy, and a random sample of 8 miles were equipped with this new mechanism and tested. These 8 missiles missed by distance with a mean of 0.76 milea and a standard deviation of 0.04 miles. Suppose that you want the probability of a Tupe I error to be 0.01. Doea the new steering system lower the miss distance?
Suppose the involved population is normal. What is the correct decision for the hypothesis test?
a) the mean miss distance is less than 0.76 miles
b) the mean miss distance is less than 0.88 miles
c) the mean miss distance is not equal to 0.88 miles
Explanation / Answer
THE NULL HYPOTHESIS = Ho= u = 0.88
the alternate hypothesis = Ha = u<0.88
alpha = 0.01
the degree of freedom = 8-1 = 7
the critical region from t table = t<-2.99
the t stat = (0.76-0.88)/(0.04/sqrt(8))
= -8.51
as the t stat = -8.51<-2.99
therefore we will reject the null hypothesis
hence we will claim that the mean miss distance is less than 0.88
hence option B is correct
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