Problems 345
47.A pharmaceutical house produces a certain drug item whose weight has a standard
deviation of .5 milligrams. The company’s research team has proposed a new
method of producing the drug. However, this entails some costs and will be
adopted only if there is strong evidence that the standard deviation of the weight
of the items will drop to below .4 milligrams. If a sample of 10 items is produced
and has the following weights, should the new method be adopted?5.728 5.731
5.722 5.719
5.727 5.724
5.718 5.726
5.723 5.72248.The production of large electrical transformers and capacitators requires the use of
polychlorinated biphenyls (PCBs), which are extremely hazardous when released
into the environment. Two methods have been suggested to monitor the levels
of PCB in fish near a large plant. It is believed that each method will result in
a normal random variable that depends on the method. Test the hypothesis at
theα=.10 level of significance that both methods have the same variance, if a
given fish is checked 8 times by each method with the following data (in parts per
million) recorded.
Method 1 6.2, 5.8, 5.7, 6.3, 5.9, 6.1, 6.2, 5.7Method 2 6.3, 5.7, 5.9, 6.4, 5.8, 6.2, 6.3, 5.549.In Problem 31, test the hypothesis that the populations have the same variances.
50.IfX 1 ,...,Xnis a sample from a normal population with varianceσx^2 , and
Y 1 ,...,Ynis an independent sample from normal population with varianceσy^2 ,
develop a significance levelαtest ofH 0 :σx^2 <σy^2 versus H 1 :σx^2 >σy^251.The amount of surface wax on each side of waxed paper bags is believed to be
normally distributed. However, there is reason to believe that there is greater
variation in the amount on the inner side of the paper than on the outside.
A sample of 75 observations of the amount of wax on each side of these bags
is obtained and the following data recorded.Wax in Pounds per Unit Area of Sample
Outside Surface Inside Surface∑ x=.948 y=.652
xi^2 = 91∑
yi^2 = 82