Question

A long-range missile missed its target by an average of 0.88mi. A new steering device is supposed to increase accuracy, and a random sample of 8 missiles were equipped with this new mechanism and tested. These 8 missiles missed by an average of 0.76 mi and a standard deviation of 0.04 mi. At α = 0.01, does the new steering mechanism lower the miss distance? (Please answer the below questions with explanation)

1) sample size of 8

2) Significance level of 0.01

Answer 1

Answer:

Given,

Consider,

Null hypothesis

Ho : = 0.88

Alternative hypothesis

H1 : < 0.88

sample size = n = 8

Test statistic = (xbar - )/(/sqrt(n))

substitute the values

= (0.76 - 0.88) / (0.04/sqrt(8))

= - 0.12/0.01414

test statistic = - 8.49

Now the corresponding p value for the required test statistic is 0.000031

Here we can say that,

p value is less than significance level i.e., 0.01

So that we reject the null hypothesis Ho

Hence we can say that, the given data provides enough evidence to support the claim that the new steering mechanism lower the miss distance at significance level = 0.01