A new rocket launching system is being considered for deployment ofsmall, short-

Question

A new rocket launching system is being considered for deployment ofsmall, short-range rockets. The existing system has p = 0.8 as theprobability of a successful launch. A sample of 1000 launches usingthe new system is made and 830 are successful. Is there reason tobelieve that the probability of a successful launch has changedwith the new system?

1. (1 pts)
   Give the null hypothesis.
   Response:
   
   
2. (1 pts)
   Give the alternative hypothesis.
   Response:
   
   
3. (1 pts)
   Calculate the p-value.
   Response:
   
   
4. (1 pts)
   At 0.01 level of significance, what would you conclude?
     Their is sufficientevidence to conclude p > 0.80
     Their is insufficientevidence to conclude p > 0.80
     Their is sufficientevidence to conclude p not = 0.80
     Their is insufficientevidence to conclude p not = 0.80

Explanation / Answer

Given n=1000, p=0.8, phat=830/1000=0.83 null hypothesis: Ho: p=0.8 alternative hypothesis Ha:p not equal 0.8 The test statistic is Z=(phat-p)/p*(1-p)/n =(0.83-0.8)/sqrt(0.8*0.2/1000) =2.37 The p-value is 2*P(Z>2.37)= 0.0177 (check normal table) Since the p-value is greater than /2=0.005, we do not rejectHo. Answer: Their is insufficient evidence toconclude p not = 0.80

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