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Answer:
a) And if we replace we got:
b)
So on this case the 99% confidence interval would be given by (62.182;93.818)
Step-by-step explanation:
Dataset given: 109 67 58 76 65 80 96 86 71 72
Part a
For this case we can calculate the sample mean with the following formula:
And if we replace we got:
And the deviation is given by:
And if we replace we got
Part b
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(0.005,9)".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 (62.182;93.818)