Question

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.)

Answer 1

Answer:

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

$df = 13-1 = 12$

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

$\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05$

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 $T = 1.782$.

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

$s = \frac{5}{\sqrt{13}} = 1.3868$

Now, we multiply T and s

$M = T*s = 1.782*1.3868 = 2.47$

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.