Space X uses multi stage rockets to get into space. In an attempt to conserve, t
ID: 3232537 • Letter: S
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 37 successful launches. They have attempted to land the first stage 25 times. In those 25 attempts, they counted 13 as successful. They will be able to save millions of dollars if they can successfully land the first stage more than 50% 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 .01 level
B) what is the power of the test if the alternative hypothesis is that they land more than 60% of the time
Explanation / Answer
(A)
mean = 0.5*25 = 12.5
std. dev. = sqrt(0.5*0.5*25) = 2.5
Below are the null and alternative hypothesis,
H0: mu <= 12.5
H1: mu > 12.5
z = (13 - 12.5)/2.5 = 0.2
p-value = 0.4201
As p-value is greater than 0.01, we fail to reject the null hypothesis. This means there are not sufficient evidence to conclude that Space X is able to land more than 50% of the time.
(B)
Beta is the probability when we fail to reject the null hypothesis i.e. type II error. As this is the right tailed test, critical value of z is 2.33.
critical value of x = 12.5 + 2.33*2.5 = 18.325
probability of X is less than 18.325 is
P(X<18.325) = P(z<(18.325 - 15)/2.5) = P(z<1.33) = 0.9082
Hence power of the test = 1 - 0.9082 = 0.0918
mu0 (hypothesised mean) 12.5 sigma 2.5 alpha 0.01 sample/true mean 15Related Questions
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