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 32 successful launches, they have attempted to land the 1st stage 23 times.

-In those 23 attempts, they counted 15 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. Test at the 0.05 level

b) What is the power of the test if the alternative hypothesis is that they can land >75% of the time.

PLEASE SHOW WORK

Explanation / Answer

Part a

Here, we have to use normal approximation to binomial distribution.

We are given n = 23, x = 15

So, P = x/n = 15/23 = 0.652174

We have to test

H0: p = 0.5 versus Ha: p 0.5

For normal approximation, we have

Mean = µ = n*p = 23*0.5 = 11.5

q = 1 – p = 1 – 0.5 = 0.5

SD = = sqrt(npq) = sqrt(23*0.5*0.5) = 2.397916

Z = (X - µ) / [/sqrt(n)]

Z =(15 – 11.5) / [2.397916/sqrt(23)]

Z = 3.5/0.5

Z = 7

P-value = 0.00 (By using Z-table or excel)

= 0.05

P-value <

So, we reject the null hypothesis

There is sufficient evidence to conclude that they are able to land more than 50% of the time.

Part b

For p = 0.75, mean = 23*0.75 = 17.25, SD = sqrt(23*0.75*0.25) = 2.076656

Z = (17.25 - 15) / 2.076656 = 1.08347266

P(Z<1.08347266) = 0.86070066

Power = 1 - 0.86070066 = 0.13929934

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