For this problem, the confidence interval is the one we are looking for. Since the confidence level is not given, we assume that it is 95%.
The formula for the confidence interval is: mean ± t (α/2)(n-1) * s √1 + 1/n
Where:
α= 5%
α/2
= 2.5%
t 0.025, 19 = 2.093 (check t table)
n = 20
df = n – 1 = 20 – 1 = 19
So plugging in our values:
8.41 ± 2.093 * 0.77 √ 1 + 1/20
= 8.41 ± 2.093 * 0.77 (1.0247)
= 8.41 ± 2.093 * 0.789019
= 8.41 ± 1.65141676
= 6.7586 < x < 10.0614
