Two hundred tires of each of four brands are individually placed in a testing apparatus and run until failure. The results are obtained the results shown in the following table:

(a) Use the 0.01 level of significance to test the null hypothesis that there is no difference in the qual-ity of the four kinds of tires with regard to their durability.

(b) Plot the four individual \(99 \%\) confidence intervals for proportions that last more than 40,000 miles.

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Brand A Brand B Brand C Brand D Failed to last 30,000 miles 26 23 15 32 Lasted from 30,000 118 93 116 121 to 40,000 Lasted more than 40,000 56 84 69 47 miles Total 200 200 200 200