Suppose that in the electric car battery example on page 242, \(n\) is changed from 36 to 50 while everything else remains the same. Find

(a) the probability of a Type I error;

(b) the probability of a Type II error when \(\mu=1680\) cycles.

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EXAMPLE 16 Tests of Hypotheses There are many problems in which, rather than estimate the value of a parameter, we must decide whether a statement concerning a parameter is true or false. Statistically speaking we test a hypothesis about a parameter. For example, in quality control work a random sample may serve to determine whether the "process mean" (for a given kind of measurement) has remained unchanged or whether it has changed to such an extent that the process has gone out of control and adjustments have to be made. Not all samples will lead to a correct assessment of water quality Refer to Example 1 of monitoring the quality of water leaving a plant. Why does evaluating a sample of specimens not always lead to correct conclusions regarding water quality?