Answer:
So on this case the 95% confidence interval would be given by (61.370;300.580)
Step-by-step explanation:
Previous concepts
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
Solution to the problem
represent the sample mean
population mean (variable of interest)
represent the sample standard deviation
n=8 represent the sample size
The confidence interval on this case is given by:
(1)
We can find the degrees of freedom and we got:
![df = n-1= 8-1=7](https://tex.z-dn.net/?f=%20df%20%3D%20n-1%3D%208-1%3D7)
The next step would be find the value of
,
and
Using the t table with df =7, excel or a calculator we see that:
![t_{\alpha/2}=2.365](https://tex.z-dn.net/?f=t_%7B%5Calpha%2F2%7D%3D2.365)
Since we have all the values we can replace:
So on this case the 95% confidence interval would be given by (61.370;300.580)