Question

Ricky is testing soil for a contaminant at a building site. He'll take action to stop construction if there's strong evidence that the soil has more than parts per million (ppm) of the contaminant. He plans on using soil from randomly selected locations at the building site. His hypotheses are and , where is the mean amount of the contaminant in the soil at this site. He's decided to use a significance level of Suppose that in reality, is actually true. Which situation below would result in the lowest probability of a Type II error?

Answer 1

Answer: Increasing the sample size (n) would result in the lowest probability of a Type II error.

Explanation: Decreasing the significance level (α): By decreasing the significance level, Ricky would require stronger evidence to reject the null hypothesis. This decreases the probability of a Type I error (rejecting the null hypothesis when it is true), but it increases the probability of a Type II error. Therefore, decreasing α would not minimize the probability of a Type II error.

Increasing the sample size (n): Increasing the sample size provides more data for the test, which can increase the power of the test. With a larger sample size, Ricky would have a better chance of detecting differences in contaminant levels if they exist. Thus, increasing the sample size would help minimize the probability of a Type II error.