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Explanation & Answer
We have a sample size of n = 7, so 6 degrees of freedom. We should use the t-distribution at 0.9 with df = 6:
t = t.inv(p=0.9, df=6) = 1.440
We also have a standard error = sample standard deviation / sqrt (sample size)
= 7.99/sqrt(7)
= 3.02
So the lower and upper values for the 80% confidence interval are given by:
mean +/- t_crit x SEM
= 17.55 +/- 1.440 x 3.02
= 17.55 +/- 4.348
= 13.20 to 21.90
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