Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. other battery models, produced by similar processes, have normally distributed life spans. the lower limit of the 90% confidence interval for the population mean life of the new model is (specify your answer to the 2nd decimal.)

The lower limit of the 90% confidence interval for the population mean life of the new model is 72.53 months.

Step-by-step explanation:

Our sample size is 13.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

Then, we need to subtract one by the confidence level and divide by 2. So:

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 12 and 0.05 in the t-distribution table, we have .

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

Now, we multiply T and s

The lower end of the interval is the mean subtracted by M. So it is 75 - 2.47 = 72.53

The lower limit of the 90% confidence interval for the population mean life of the new model is 72.53 months.

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