Answer:
a) The 99% confidence interval would be given by (346.708;453.292)
b) The 99% confidence interval would be given by (338.445;461.555)
Step-by-step explanation:
1) Previous concepts
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".
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".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n=15 represent the sample size
2) Part a
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (346.708;453.292)
3) Part b
For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.
The confidence interval for the mean is given by the following formula:
(1)
We need to find the degrees of freedom first df=n-1=15-1=14
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (338.445;461.555)