If the cost of a Type I error is high, a bigger value should be chosen for the _____.

Question

If the cost of a Type I error is high, a bigger value should be chosen for the  _____.

BlackTom AI · Accepted Answer

We are given a question about decision rules in hypothesis testing and the relative costs of errors. The prompt asks where a bigger value should be chosen when the cost of a Type I error is high.
Option 1: test statistic. This is a computed value from the sample data (e.g., z, t, etc.). Its magnitude is not set by a chosen value to control error rates; it depends on the data. Therefore, increasing a test statistic value is not the mechanism used to adjust the balance between Type I and Type II errors.
Option 2: critical value. The critical value is the threshold that the test statistic must exceed to reject the null hypothesis. While the critical value does change with the chosen significance level, simply stating to pick a bigger critical value is not a standalone decision; it is determined by the significance level, and a bigger threshold typically corresponds to a smaller alpha. However, the question asks about a parameter you deliberately choose to control error cost, not a byproduct of another choice.
Option 3: confidence coefficient. The confidence coefficient is the complement of the level of significance (alpha) and defines the confidence level (e.g., 90%, 95%, 99%). A higher confidence coefficient means a higher confidence level and thus a smaller alpha, which reduces the probability of a Type I error. When the cost of a Type I error is high, you purposefully select a larger confidence coefficient to tighten the chance of a false positive.
Option 4: level of significance. The level of significance is alpha, the threshold for rejecting the null hypothesis. Increasing alpha raises the probability of a Type I error, which is contrary to the goal of reducing such errors when their cost is high. Therefore, one would not choose a bigger alpha in this context.
In summary, the mechanism to reduce the likelihood of a Type I error by design is to opt for a higher confidence level, i.e., a bigger confidence coefficient, which corresponds to a smaller alpha and tighter criteria for rejection. The other options either depend on sample data in a way that does not directly reflect error-cost control, or they move in the direction of increasing Type I error rather than reducing it.

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If the cost of a Type I error is high, a bigger value should be chosen for the _____.

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