Answer:
So on this case the 99% confidence interval would be given by (130.77;196.89)
Step-by-step explanation:
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".
Data: 175 177 175 180 138 138
We can calculate the mean and the deviation from these data with the following formulas:
represent the sample mean for the sample
population mean (variable of interest)
s=20.093 represent the sample standard deviation
n=6 represent the sample size
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value 
we need to find first the degrees of freedom, given by:
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(0.005,5)".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 (130.77;196.89)
