Answer to Question #169488 in Statistics and Probability for Sunera

Question

A manufacturer of a brand of designer jeans realizes that many retailers charge less than the suggested retail price of $40. A random sample of 20 retailers reveals that the mean and the standard deviation of the prices of the jeans are $32 and $2.50 respectively. Estimate with 90% confidence the mean retail price of the jeans.

Answer 1

$c = 90 \;\% = 0.90 \\ \bar{x}=32 \\ σ = 2.50 \\ n = 20 \\ df = n-1 = 19 \\ α = \frac{1-c}{2} = 0.05$

$t_{α/2} = 1.328$ (from t Table)

The margin error is:

$E = t_{α/2} \times \frac{s}{\sqrt{n}} = 1.328 \times \frac{2.50}{\sqrt{20}} = 0.742$

The mean retail price of the jeans with 90% confidence = 32±0.74