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Answer:
The 95% confidence interval would be given by (6.03;7.49)
Step-by-step explanation:
Notation
represent the sample mean
population mean (variable of interest)
s represent the sample standard deviation
n=50 represent the sample size
Solution
The confidence interval for the mean is given by the following formula:
(1)
We can calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
In order to calculate the critical value we need to find first the degrees of freedom, given by:
We assume a standard confidence level of 0.95 or 95%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that
Now we have everything in order to replace into formula (1):
The 95% confidence interval would be given by (6.03;7.49)