Question

2. One important factor in inventory control is the variance of the daily demand for a product. Management believes that demand is normally distributed with the variance equal to 250. In an experiment to test this belief about , the daily demand was recorded for 25 days. The data has been summarized as follows: xbar = 50.6 and s2 = 500 Do the data provide sufficient evidence to show that management's belief about the variance is untrue? (Use alpa=0.01 ).

Answer 1

we reject H0 and conclude that management's belief about variance is untrue.

Explanation:

H0 : σ² = 250

H1 : σ² ≠ 250

Sample size, n = 25

xbar = 50.6 ; s² = 500

α = 0.01 ;

The test statistic :

χ² = [(n - 1)s²] ÷ σ²

χ² = [(25 - 1)* 500] ÷ 250

χ² = (24 * 500) / 250

χ² = 12000 / 250

χ² = 48

The critical value:

df = n-1 ; 25 - 1 = 24

χ²(0.01/2 ; 24) = 45.559

Decison :

Reject H0 : if |χ² statistic| > critical value

Since 48 > 45.559

Hemce, we reject H0 and conclude that management's belief about variance is untrue.