STA$4820/012/0/2024$

QUESTION $6$

$[9]$

One important factor in inventory control is the variance of the daily demand for the product. A management scientist has developed the optimal order quantity and reorder point, assuming that the variance is equal to $250.$ Recently, the company has experienced some inventory problems, which induced the operations manager to doubt the assumption. To examine the problem, the manager took a random sample of $25$ days and recorded the demand. The demand sample variance was $s^2=270\mathrm{.}58.$

a$.$ Do these data provide sufficient evidence at the $5\%$ significance level to infer that the management scientist's assumption about the variance was wrong?

b$.$ What are the required assumptions for the statistical procedure in part a to be valid?

$(1)$

c$.$ Does it appear that the required condition is not satisfied?

$(1)$