Subjects statistics

Hypothesis Identification

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Hypothesis Identification


1. The problem asks us to identify which scenario matches the null hypothesis $p \geq 0.44$ and the alternative hypothesis $p < 0.44$. 2. The null hypothesis $p \geq 0.44$ means the parameter $p$ (proportion of internet users participating in social media) is at least 44%. 3. The alternative hypothesis $p < 0.44$ means the claim is that this proportion is actually less than 44%. 4. Now, let's examine the options: - Option 1 says an article is trying to show less than 44%, contrary to an established figure saying at least 44%. This matches $H_0: p \geq 0.44$ and $H_a: p < 0.44$. - Option 2 says the article is trying to show exactly 44%, which does not reflect one-sided alternative $p < 0.44$. - Option 3 involves showing more than 44%, contrary to at most 44%, which corresponds to $p > 0.44$ vs $p \leq 0.44$, the reverse case. - Option 4 is showing at least 44%, contrary to less than 44%, again the opposite setup. 5. Therefore, the correct choice is Option 1, which aligns with the null hypothesis $p \geq 0.44$ and alternative $p < 0.44$. Final answer: An online article trying to show that less than 44% of internet users participate in social media, contrary to an established figure saying at least 44% participate.