Since we don't know the population standard deviation, only that for the sample, we should use a t-distribution here, with df = n-1 = 399. The critical t-stat for a 99% confidence interval will be:
t_crit = t.inv(p=0.995,df=399) = 2.588207164
The standard error is sample sd / sqrt(n) = 2.7/sqrt(400)
SEM = 0.135
So the 99% confidence interval for the sample mean is given by
sample mean +/- t_crit x SEM
= 8.84 +/- 2.588 x 0.135
= [8.4906 to 9.1894]
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