Suppose that samples of size 1

Suppose that samples of size 1, 2, and 3 are independently selected from three different populations. Let ­i and i (i  1, 2, 3) denote the population means and standard deviations, and consider estimating   where the i s are specified numerical constants. A point estimate of  is   When the sample sizes are all large,  has approximately a normal distribution with variance

An estimated variance s2   results from replacing the 2 s; by the s2 s;  can then be standardized to obtain a z variable from which the confidence interval    (z crit) is obtained. Suppose that samples of three different brands of tires with identical lifetime ratings—a store brand (1) and two national brands (2 and 3)—are selected, and the lifetime of each tire is determined, resulting in the following data:

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