Space X uses multi-stage rockets to get into space. In an attempt to conserve, t

Question

Space X uses multi-stage rockets to get into space. In an attempt to conserve, they try to land the 1st stage after use so they can reuse this in 30 successful launches. They have attempted to land the 1st stage 21 times. In those 21 attempts, they counted 13 as successful. They will be able to save millions of dollars if they can successfully land the 1st stage > 50 percent of the time.

a) Using the normal approximation to the binomial, test the alternative hypothesis that they are able to land more than 50% of the time at the 0.01 level.

b) What is the power of the test if the alternative hypothesis is that they can land > 80% of the time

Explanation / Answer

(A)

here mean = 21 * 0.5 = 10.5

std. dev. = sqrt(0.5*0.5*21) = 2.29

below are the null and alternate hypothesis

H0: mu <= 10.5

H1: mu > 10.5

Test statistics, z = (13 - 10.5)/2.29 = 1.0917

p-value = 0.1375

As p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis. This means there is not sufficient evidence to conclude that they are able to land more than 50%.

(B)

In order to determine the power of the test, lets first find out the the type II error.'

As this is right tailed test, z-value for 0.01 significance level is 2.33

critical value of x is = 10.5 + 2.33*2.29 = 15.84

Type II error will occur when we fail to reject the null hypothesis. This means we need to find P(X<15.84) for mean = 16.8 (=0.8*21). and sigma = 2.29

P(X<15.84) = P(z<(16.8 - 15.84)/2.29) = P(z < 0.4192) = 0.6625 (This is type II error)

Hence power of the test is 1 - 0.6625 = 0.3375

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