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
[tex]df = 13-1 = 12[/tex]
Then, we need to subtract one by the confidence level [tex]\alpha[/tex] and divide by 2. So:
[tex]\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05[/tex]
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 [tex]T = 1.782[/tex].
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
[tex]s = \frac{5}{\sqrt{13}} = 1.3868[/tex]
Now, we multiply T and s
[tex]M = T*s = 1.782*1.3868 = 2.47[/tex]
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.
