Which of these statements is always true for a researcher who is using standard statistical
methods in a test of significance?
A. A researcher who rejects a true null hypothesis has committed a Type II error.
B. A researcher who rejects the null hypothesis has computed a test statistic that is negative
in value.
C. A researcher who rejects the null hypothesis has computed a P-value that is large in
value.
D. Increasing the sample size affects the probability of making a Type I error.
E. None of the above is true.
I have been trying this problem for hours and cannot understand it. Please help
To determine which statement is always true for a researcher using standard statistical methods in a test of significance, let's analyze each statement.
A. The statement "A researcher who rejects a true null hypothesis has committed a Type II error" is incorrect. When a researcher rejects a true null hypothesis, it means they have correctly identified an effect or difference in the population. This is known as a correct rejection or a significant result, not a Type II error.
B. The statement "A researcher who rejects the null hypothesis has computed a test statistic that is negative in value" is not always true. The value of the test statistic depends on the nature of the hypothesis test and the specific research question. It can be positive, negative, or zero, depending on the data and the alternative hypothesis.
C. The statement "A researcher who rejects the null hypothesis has computed a P-value that is large in value" is also incorrect. Rejecting the null hypothesis generally indicates that the obtained result is statistically significant, which means the P-value is small (typically less than a chosen significance level, such as 0.05).
D. The statement "Increasing the sample size affects the probability of making a Type I error" is correct. As the sample size increases, the precision and reliability of the estimate improve, reducing the probability of making a Type I error (rejecting a true null hypothesis).
E. The correct answer to the question is therefore option D: Increasing the sample size affects the probability of making a Type I error.
To arrive at this answer, it is important to understand the concepts of Type I and Type II errors, null hypothesis, alternative hypothesis, test statistics, P-values, and the relationship between sample size and errors in hypothesis testing. Reviewing these concepts will help in solving similar problems in the future.