Question

a researcher wants to avoid making a type ii error. which of the following actions would be the most effective in reducing the risk of a type ii error?
a. ○ increase the sample size.
b. ○ choose an alpha level of 0.01.
c. ○ choose an alpha level of 0.05.

Explanation:

• Type II error: It is the failure to reject a false null hypothesis.
• Sample size: A larger sample size provides more information about the population. With more data, the test has more power to detect a true effect (i.e., reject a false null hypothesis). Mathematically, the standard error ($\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$) decreases as \(n\) (sample size) increases. A smaller standard error makes it easier to detect differences between the sample statistic and the hypothesized value under the null hypothesis.
• Alpha level: The alpha level (\(\alpha\)) is the probability of making a Type I error (rejecting a true null hypothesis). A lower \(\alpha\) (e.g., \(\alpha = 0.01\)) makes it harder to reject the null hypothesis (increases the critical value in hypothesis - testing), which in turn increases the probability of Type II error (\(\beta\)). A higher \(\alpha\) (e.g., \(\alpha=0.05\)) makes it easier to reject the null hypothesis, but it mainly affects Type I error probability and has a less direct and less powerful impact on reducing Type II error compared to increasing the sample size.

Answer:

A. Increase the sample size.