If a hypothesis test for a single population variance is to be conducted, which of the following statements is true?
A) The null hypothesis must be stated in terms of the population variance.
B) The chi-square distribution is used.
C) If the sample size is increased, the critical value is also increased for a given level of statistical significance.
D) All of the above are true.

Question

Quizplus · Accepted Answer

All the statements are true regarding a hypothesis test for a single population variance: A) correctly identifies that the null hypothesis is stated in terms of the population variance, B) correctly notes that the chi-square distribution is used in this context, and C) is incorrect in suggesting that increasing the sample size increases the critical value; in fact, increasing the sample size generally makes the test more sensitive (i.e., able to detect smaller differences) without necessarily changing the critical values, which are determined by the chosen level of significance and the degrees of freedom (which are indeed affected by sample size but not in a way that directly increases critical values as implied). My explanation contains an error regarding statement C, which might have led to confusion. Let's correct that: The critical value in the context of hypothesis testing, especially with chi-square distributions, is determined by the level of significance and the degrees of freedom (which are indeed affected by sample size). However, the relationship between sample size and critical values is not as directly stated in option C. The critical values for a given level of significance are determined by the distribution and the degrees of freedom, which for a chi-square test, depend on the sample size minus one. However, the statement as phrased in C about the critical value increasing with sample size for a given level of significance is misleading in this context. The correct understanding is that while sample size affects the degrees of freedom, and thus indirectly influences the distribution used to determine critical values, it does not directly cause an increase in critical values in the manner suggested.

If a Hypothesis Test for a Single Population Variance Is