Applied Engineering Statistics Exam

IE5002 Homework 2

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1. An article in IEEE International Symposium on Electromagnetic Compatibility (Vol. 2,

2002, pp. 667–670) describes the quantification of the absorption of electromagnetic

energy and the resulting thermal effect from cellular phones. The experimental results

were obtained from in vivo experiments conducted on rats. The arterial blood pressure

values (mmHg) for the control group (8 rats) during the experiment are �� � th��� � t

and for the test group (9 rats) are �� � ��t��� � �h.�� � h�ht�

(a) Is there evidence to support the claim that the test group has higher mean blood

pressure? Assume that both populations are normally distributed, but the variances are not

equal.

(b) Calculate a confidence interval to answer the question in part (a).

2. The diameter of steel rods manufactured on two different extrusion machines is being

investigated. Two random samples of sizes n1=15 and n2 = 17 are selected, and the sample

means and sample variances are �� � e�ns��� � � h�stQ �� � e��e���

� � h��h respectively.

Assume that �� � � ��

� and that the data are drawn from a normal distribution. �� � h�ht�

(a) Is there evidence to support the claim that the two machines produce rods with

different mean diameters?

(b) Construct a 95% CI for the difference in mean rod diameter. Interpret this interval.

3. Fifteen adult males between the ages of 35 and 50 participated in a study to evaluate the

effect of diet and exercise on blood cholesterol levels. The total cholesterol was measured

in each subject initially, and then 3 months after participating in an aerobic exercise

program and switching to a low-fat diet, as shown in the following table. �� � h�ht�

(a) Do the data support the claim that low-fat diet and aerobic exercise are of value in

IE5002 Homework 2

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producing a mean reduction in blood cholesterol levels?

(b) Find a 95% CI on the mean reduction in blood cholesterol level.

4. In semiconductor manufacturing, wet chemical etching is often used to remove silicon

from the backs of wafers prior to metallization. The etch rate is an important

characteristic in this process and known to follow a normal distribution. Two different

etching solutions have been compared, using two random samples of 10 wafers for etch

solution. The observed etch rates are as follows (in mils/min):

Test the hypothesis H0: �� � � ��

� against H1: �� � � ��

� using � � h�ht and draw

conclusions.