Question

In: Statistics and Probability

The service life of a battery used in a cardiac pacemaker is assumed to be normally...

  1. The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A sample of twelve 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: 26.9, 26.4, 26.8, 24.5, 24.9, 28.4, 25.4, 27.8, 27.5, 24.9, 26.9, and 25.5. Test the hypothesis that the mean battery life exceeds 25 hours.
  1. State the null and alternative hypothesis.

  1. Compute the test statistics.

  1. Compute the P-value.

  1. State a conclusion
  1. Construct a 95% two-sided confidence interval on mean life in the accelerated test.

Solutions

Expert Solution

sr.no. x x-x̅ (x-x̅)^2
1 26.9 0.575 0.330625
2 26.4 0.075 0.005625
3 26.8 0.475 0.225625
4 24.5 -1.825 3.330625
5 24.9 -1.425 2.030625
6 28.4 2.075 4.305625
7 25.4 -0.925 0.855625
8 27.8 1.475 2.175625
9 27.5 1.175 1.380625
10 24.9 -1.425 2.030625
11 26.9 0.575 0.330625
12 25.5 -0.825 0.680625
Total 315.9 17.6825
mean=x̅ Total/12
             x̅= 26.325

orchestra answered 2 years ago
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