Develop the \"statistics\" to answer the questions posed below. Construct an app

Question

Develop the "statistics" to answer the questions posed below. Construct an appropriate confidence interval. State and check all assumptions and conditions before proceeding with any tests. support your results in the spaces provided. computer components, Inc. has found that historically the mean time between failures of hardware that is produces is 520 hours. In an effort ot increase perfomnace, the company makes a change to its manufactureing process. Afterwards , it tests 10 randomly selected computers and meansures the time between failures. he results follows ( in hours): 518,548,561,523,536,563,528,557,538,and 449. 1. discuss the company's claim that it has, indeed, improved performance. 2. CCI wants to estimate within 5 hours and with 95% confidence the new time between failures. how large a sample must they consider in order to do so?

Explanation / Answer

from above test stat t=(X-mean)/std error =(532.11-520)/10.488=1.1547

for above p value at 9 degree of freedom = 0.1389

as p value is greater then 0.05 level, we can not reject that mean from 520 has changed and hence can not accept company's claim.

2) here std deviation of new process S=33.167.

also margin of error E=5

for 95%CI; z=1.96

hence sample size =(S*Z/E)2=(33.167*1.96/5)2=169.03~170

X 518.000 548.000 561.000 523.000 536.000 563.000 528.000 557.000 538.000 449.100 mean(X) 532.110 std deviation(S) 33.167 std error =S/(n)1/2 10.488

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