In general, increasing the sample size (for example, from n = 4 to n = 50) will ____ the risk of a Type I error. (Assume alpha is held constant at .05.)

Select one:
a. decrease
b. increase
c. have no influence on

SEm (standard error of the mean) = SD/√n

The correct answer is c. have no influence on.

To understand why increasing the sample size does not influence the risk of a Type I error, we need to understand what a Type I error is and how it is related to sample size.

A Type I error occurs when we falsely reject a true null hypothesis. In hypothesis testing, we set a significance level (denoted as alpha) to determine the threshold at which we consider the evidence against the null hypothesis to be statistically significant. The commonly used value for alpha is 0.05, which means that we are willing to accept a 5% chance of making a Type I error.

The risk of a Type I error is primarily determined by the significance level (alpha) chosen before conducting the hypothesis test. It is not directly influenced by the sample size.

Increasing the sample size has several advantages, such as increasing the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false. A larger sample size can provide more precise estimates and reduce the margin of error. However, the risk of Type I error remains constant as long as the significance level (alpha) is held constant.

To summarize, increasing the sample size will not decrease or increase the risk of a Type I error. The risk of a Type I error is determined by the chosen significance level (alpha) and not influenced by the sample size.