99% confidence interval for the mean

16.3 ± 0.8391

Step-by-step explanation:

The confidence interval is:

CI = x ± SE * CV

where x is the sample mean, SE is the standard error, and CV is the critical value (either t score or z score).

Here, x = 16.3.

The standard error for a sample mean is:

SE = σ / √n

SE = 1.5 / √25

SE = 0.3

The critical value is looked up in a table or found with a calculator.  But first, we must find the alpha level, the critical probability, and the degrees of freedom.

α = 1 - 0.99 = 0.01

p* = 1 - (α/2) = 1 - (0.01/2) = 0.995

df = n - 1 = 25 - 1 = 24

Since df < 30, we use a t-score.  Looking up in a t-table, we find the critical value is CV = 2.797.

Therefore:

CI = 16.3 ± (0.3 * 2.797)

CI = 16.3 ± 0.8391