Answer:
16.3 ± 0.8391
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