A pharmaceutical manufacturer purchases a particular

Chapter 10, Problem 123SE

(choose chapter or problem)

A pharmaceutical manufacturer purchases a particular material from two different suppliers. The mean level of impurities in the raw material is approximately the same for both suppliers, but the manufacturer is concerned about the variability of the impurities from shipment to shipment. If the level of impurities tends to vary excessively for one source of supply, it could affect the quality of the pharmaceutical product. To compare the variation in percentage impurities for the two suppliers, the manufacturer selects ten shipments from each of the two suppliers and measures the percentage of impurities in the raw material for each shipment. The sample means and variances are shown in the accompanying table.

Supplier A	Supplier B
\(\overline{y_{i}}=1.89\)	\(\overline{y_{2}}=1.85\)
\(s_{1}^{2}=.273\)	\(s_{2}^{2}=.094\)
\(n_{1}=10\)	\(n_{2}=10\)

a Do the data provide sufficient evidence to indicate a difference in the variability of the shipment impurity levels for the two suppliers? Test using  Based on the results of your test, what recommendation would you make to the pharmaceutical manufacturer?

b Find a  confidence interval for \(\sigma_{B}^{2}\) and interpret your results.

Equation transcription:

Text transcription:

overline{y{i}}=1.89

overline{y{2}}=1.85

s{1}^{2}=.273

s{2}^{2}=.094

n{1}=10

n{2}=10

sigma{B}^{2}