For the following, indicate whether the probability of a Type II error (i. E., b

Question

For the following, indicate whether the probability of a Type II error (i. E., beta) increases, decreases, or remains the same. I recommend drawing a figure showing the null and reality curves and shading the regions corresponding to the probabilities of Type I and Type II errors to help think about this. The probability of a Type I error (i. E., alpha) is changed from 0.01 to 0.05, but the sample size (i. E., n) is held constant. The sample size increases, but the probability of a Type I error remains constant. Both sample size and the probability of a Type I error remain constant, but the difference between the null hypothesis value and the "true" value (i. E. the effect size) increases. Both sample size and the probability of a Type I error remain constant but you conduct a two-sided test rather than a one-sided test.

Explanation / Answer

a) if alpha change from 0.01 to 0.05 and sample size n is constand then

              Probability of Type II error decreases

b) if sample size increases and probability of type I error remains constant then

              Probability of Type II error decreases

c) Both sample size and the probability of a Type I error remain constant, but difference increases

          then probability of Type II error decreases

d) Both sample size and P(type I error) remain constant, change two-sided test one-sided test.

              Then probability of Type II error decreases

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