Question

Find the boundary of the critical region if the type i error probability is as given below. Note: we are finding the critical value for the one-sided test x £ 12 − za 0.5/ n

(a) = 0.01 and = 4
(b) = 0.01 and = 16
(c) = 0.05 and = 4
(d) = 0.05 and = 16

Answer 1

To determine the boundary of the critical region with a specified Type I error probability (α), locate the z-score on the standard normal distribution that corresponds to the given α for a one-sided test. Use the z-score and sample size to establish the critical value at which the null hypothesis is rejected.

Step-by-step explanation:

To find the boundary of the critical region with a given Type I error probability (α), we use the standard normal distribution (Z-distribution). The critical value corresponds to the z-score which divides the area under the curve into a central region and the critical region (tail).

The steps to find the critical value are:

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5. 
   

Given examples for Type I error probability α and sample size n:

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To provide an example, if α = 0.05, the z-score would be approximately -1.645. Hence, if the test statistic calculated is to the left of -1.645, we would reject the null hypothesis.