Question

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.

2. Compute the test statistics.

3. Compute the P-value.

4. State a conclusion

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

Answer 1

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