Multiple Choice
Which of the following is not a criterion for making a decision in a hypothesis test?
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
Multiple Choice
Which of the following is not true about -values in hypothesis testing?
A
A -value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.
B
If the -value is less than the significance level, we reject the null hypothesis.
C
A small -value indicates strong evidence against the null hypothesis.
D
A -value tells us the probability that the null hypothesis is true.
Verified step by step guidance1
Step 1: Understand the definition of a p-value. A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. This means it measures how compatible the data is with the null hypothesis.
Step 2: Recognize the decision rule in hypothesis testing. If the p-value is less than the chosen significance level (\$\(\alpha\)\$), we reject the null hypothesis because the observed data is unlikely under the null hypothesis.
Step 3: Interpret what a small p-value means. A small p-value indicates strong evidence against the null hypothesis, suggesting that the observed data is unlikely to have occurred if the null hypothesis were true.
Step 4: Identify the incorrect statement. The statement that a p-value tells us the probability that the null hypothesis is true is incorrect because the p-value assumes the null hypothesis is true and does not provide the probability of the hypothesis itself.
Step 5: Summarize that p-values do not measure the probability of the null hypothesis being true or false; rather, they measure the probability of the observed data under the assumption that the null hypothesis is true.
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