How do you do this question
A 95% confidence interval for the population mean based on a sample 109 observations is 48.26 to 52.39. Which of the following is most likely the 99% confidence interval?
A 48. 60 to 52.05
B 52.39 to 56.85
C 47.59 to 53.06
How do you work this out it’s 47.59 to 53.06
50.325 is the mean, given that the degrees of freedom is quite high (108 as n= 109), you can assume a normal distribution.
52.39 - 50.325= 2.065 which represents 1.96 standard deviations (since this is the 95% CI).
Hence 1 standard deviation= 1.05357...
From the normal distribution, 99% CI is 2.58 standard deviations above or below the mean.
Hence upper fence of 99% CI= 50.325 + (2.58 x 1.05357...)= 53.04
And lower fence of 99% CI= 50.325 - (2.58 x 1.05357...)= 47.61
Which is the closest to option C. Note that I used the stats table provided in my uni physical + analytical chem unit so there's some minor rounding differences depending on which version of the table you use.