The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7. The manufacturer wants to be certain that the mean battery life exceeds 25 hours in accelerated lifetime testing. Construct a 90%, two sided confidence interval on mean life in the accelerated test.

The confidence interval is  

Step-by-step explanation:

From  the question we are given a data set

     25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is  

where is the sample size with values  n =  10

The standard deviation is evaluated as

substituting values

The  confidence level is given as 90% hence the level of significance is calculated as

    %

Now the critical values of is obtained from the normal distribution table as

The reason  we are obtaining  the critical values of instead of   is because  we are considering two tails of the area under the normal curve

  The margin of error is evaluated as

substituting values

The  90%, two sided confidence interval is mathematically evaluated as

Given that the lower and the upper limit is greater than  25 then we can assure the manufactures  that the battery life exceeds 25 hours

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