Answer:
The 95% confidence interval would be given by (4.729;5.271)
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".
The standard error of a statistic is "the standard deviation of its sampling distribution or an estimate of that standard deviation"
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)
s represent the sample standard deviation
n represent the sample size
The confidence interval for the mean is given by the following formula:
(1)
We use the t distirbution for this case since we don't know the population standard deviation .
Where the standard error is given by:
And the margin of error would be given by:
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. And we see that
The standard error would be given by:
Now we have everything in order to replace into formula (1) and calculate the interval:
So on this case the 95% confidence interval would be given by (4.729;5.271)