Introduction to Probability and Statistics for Engineers and Scientists

472 Chapter 10:Analysis of Variance

Filter No. 1 Filter No. 2 Filter No. 3

82 86 85

93 89 97

90 92 90

96 98 87

87 95 90

99 102 101

101 105 100

79 85 84

98 97 102

Test, at the 5 percent level of significance, the hypothesis that the filters are the

same.

3. Explain why we cannot efficiently test the hypothesisH 0 :μ 1 =μ 2 = ··· =μm
   by runningt-tests on all of the

(m

2

)

pairs of samples.

4. A machine shop contains 3 ovens that are used to heat metal specimens. Subject to
   random fluctuations, they are all supposed to heat to the same temperature. To test
   this hypothesis, temperatures were noted on 15 separate heatings. The following
   data resulted.

Oven Temperature

1 492.4, 493.6, 498.5, 488.6, 494

2 488.5, 485.3, 482, 479.4, 478

3 502.1, 492, 497.5, 495.3, 486.7

Do the ovens appear to operate at the same temperature? Test at the 5 percent

level of significance. What is thep-value?

5. Four standard chemical procedures are used to determine the magnesium content
   in a certain chemical compound. Each procedure is used four times on a given
   compound with the following data resulting.

Method

1234

76.42 80.41 74.20 86.20

78.62 82.26 72.68 86.04

80.40 81.15 78.84 84.36

78.20 79.20 80.32 80.68

Do the data indicate that the procedures yield equivalent results?