Respuesta :
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
[tex]df = 96-1 = 95[/tex]
Then, we need to subtract one by the confidence level [tex]\alpha[/tex] and divide by 2. So:
[tex]\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025[/tex]
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 [tex]T = 1.9855[/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{5.6}{\sqrt{96}} = 0.57[/tex]
Now, we multiply T and s
[tex]M = T*s = 1.9855*0.57 = 1.31[/tex]
For the lower end of the interval, we subtract the mean by M. So [tex]19.6 - 1.31 = 18.29[/tex]
For the upper end of the interval, we add the mean to M. So [tex]19.6 + 1.31 = 20.91[/tex]
The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).
