Answer:
The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).
Step-by-step explanation:
Our sample size is 96.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
![df = 96-1 = 95](https://tex.z-dn.net/?f=df%20%3D%2096-1%20%3D%2095)
Then, we need to subtract one by the confidence level
and divide by 2. So:
![\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025](https://tex.z-dn.net/?f=%5Cfrac%7B1-0.95%7D%7B2%7D%20%3D%20%5Cfrac%7B0.05%7D%7B2%7D%20%3D%200.025)
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 95 and 0.025 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
![s = \frac{5.6}{\sqrt{96}} = 0.57](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B5.6%7D%7B%5Csqrt%7B96%7D%7D%20%3D%200.57)
Now, we multiply T and s
![M = T*s = 1.9855*0.57 = 1.31](https://tex.z-dn.net/?f=M%20%3D%20T%2As%20%3D%201.9855%2A0.57%20%3D%201.31)
For the lower end of the interval, we subtract the mean by M. So ![19.6 - 1.31 = 18.29](https://tex.z-dn.net/?f=19.6%20-%201.31%20%3D%2018.29)
For the upper end of the interval, we add the mean to M. So ![19.6 + 1.31 = 20.91](https://tex.z-dn.net/?f=19.6%20%2B%201.31%20%3D%2020.91)
The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).