Question

Market research indicates that a new product has the potential to make the company an additional $1.6 million, with a standard deviation of $2.5 million. If these estimates were based on a sample of 12 customers from a normally distributed data set, what would be the 95% confidence interval

Answer 1

(0.01, 3.19)

Explanation:

Given that :

Mean (m) = 1.6 million

Standard deviation (s) = 2.5 million

α = 0.05

Sample size (n) = 12

Confidence interval :

m ± t(α, df = n - 1) * standard error

Standard Error = s/√n = 2.5 / √12 = 0.7216878

t0.05,11 = 2.200985 (t value calculator)

Hence,

1.6 ± 2.200985(0.7216878)

Lower bound /

1.6 - 2.200985(0.7216878) = 0.011575977517

Upper bound:

1.6 + 2.200985(0.7216878) = 3.188424022483

(0.01, 3.19)