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The lifetimes in hours of two brands of batteries follow normal distributions with means (miu x, miu y) respectively and unequal variances. Independent random samples

The lifetimes in hours of two brands of batteries follow normal distributions with means (miu x, miu y) respectively and unequal variances. Independent random samples of 5 batteries from each brand are taken and the following data is observed. n= 40

Brand n Sample mean sample variance
A 40 210 840
B 40 190 760

Test at the 5% significance level the null hypothesis that the means are equal against the alternative that they are not. The value of the test statistic and the decision are

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