Introduction to Probability and Statistics for Engineers and Scientists

340 Chapter 8:Hypothesis Testing

when the population standard deviations areσ 1 =10and

(a)σ 2 =5;(b)σ 2 = 10;(c)σ 2 = 20.

30.The data below give the lifetimes in hundreds of hours of samples of two types of

electronic tubes. Past lifetime data of such tubes have shown that they can often be

modeled as arising from a lognormal distribution. That is, the logarithms of the

data are normally distributed. Assuming that variance of the logarithms is equal

for the two populations, test, at the 5 percent level of significance, the hypothesis

that the two population distributions are identical.

Type 1 32, 84, 37, 42, 78, 62, 59, 74

Type 2 39, 111, 55, 106, 90, 87, 85

31.The viscosity of two different brands of car oil is measured and the following data

resulted:

Brand 1 10.62, 10.58, 10.33, 10.72, 10.44, 10.74

Brand 2 10.50, 10.52, 10.58, 10.62, 10.55, 10.51, 10.53

Test the hypothesis that the mean viscosity of the two brands is equal, assuming

that the populations have normal distributions with equal variances.

32.It is argued that the resistance of wire A is greater than the resistance of wire B.

You make tests on each wire with the following results.

Wire A Wire B

.140 ohm .135 ohm

.138 .140

.143 .136

.142 .142

.144 .138

.137 .140

What conclusion can you draw at the 10 percent significance level? Explain what

assumptions you are making.

In Problems 33 through 40, assume that the population distributions are normal

and have equal variances.

33.Twenty-five men between the ages of 25 and 30, who were participating in a well-

known heart study carried out in Framingham, Massachusetts, were randomly

selected. Of these, 11 were smokers and 14 were not. The following data refer to

readings of their systolic blood pressure.