When the p-value is less than alpha, we should reject the null hypothesis.

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The statement to evaluate is: 'When the p-value is less than alpha, we should reject the null hypothesis.'

First, recall the core decision rule in null hypothesis significance testing: compare the observed p-value to the pre-specified significance level alpha. If p-value ≤ alpha, the result is considered statistically significant and we reject the null hypothesis. If p-value > alpha, we fail to reject the null hypothesis.

In this sense, a p-value smaller than alpha indicates that the observed data would be unlikely under the null model, providing evidence against H0 and leading to rejection. This is the standard justification for using the p-value as a measure of evidence against the null.

A few common misconceptions to watch out for: 
- The p-value is not the probability that the null hypothesis is true. It is the probability, assuming H0 is true, of obtaining data as extreme as or more extreme than what was observed.
- Rejecting H0 at alpha does not prove the alternative hypothesis; it only provides evidence against the null within the specified alpha level.
- The choice of alpha affects the stringency of the test; a smaller alpha makes it harder to reject H0, even if the p-value is moderately small.

Because the provided answer choices are missing, we can nonetheless affirm that the correct content-matching choice would be the one stating that a p-value below alpha leads to rejection of the null hypothesis. If a true/false option exists, 'True' aligns with the standard interpretation of the p-value rule.

STAT 1450.02 SP2025 (28132) Checkpoint 17.3

When the p-value is less than alpha, we should reject the null hypothesis.

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STAT 1450.02 SP2025 (28132) Checkpoint 17.3

When the p-value is less than alpha, we should reject the null hypothesis.

View Explanation

Log in for full answers

Similar Questions

Which one is true?

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

For a given sample, the P-value for upper tail test is x, and the P-value for two-tailed test is y, then

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

For a sample size of 30, changing from using the t distribution to using the standard normal distribution in a hypothesis test _____.

Exhibit 9-5 n = 16 H0: μ ≥ 80 = 75.607 Ha: μ < 80 σ = 8.6 Assume the population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to _____.

Exhibit 9-1 ​ ​ Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter? c08.p089.q0008

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Stylized Writing Assistant

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Past Exam Questions by School

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Exhibit 9-1 Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.