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Explanation & Answer
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 = 24. The critical t-stat for a 98% confidence interval will be:
t_crit = t.inv(p=0.99,df=24) = 2.492159473
The standard error is sample sd / sqrt(n) = 8/sqrt(25)
SEM = 1.6
So the 98% confidence interval for the sample mean is given by
sample mean +/- t_crit x SEM
= 173 +/- 2.492159473 x 1.6
= [169.01 to 176.99]
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