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5/22 We want to test if LSPU students take more than four years to graduate from high school. State the alternative hypothesis. Ha: \( \mu<4 \) Ha: \( \mu>4 \) Emilio Mejia

Ask by Bryant Davies. in Puerto Rico
Mar 13,2025

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The alternative hypothesis is \( \mu > 4 \).

Solution

To state the alternative hypothesis for the given scenario, we need to clarify what we are testing. The problem states that we want to test if LSPU students take more than four years to graduate from high school. In hypothesis testing, the alternative hypothesis (\(H_a\)) represents the claim that we are trying to find evidence for. Since we are interested in whether LSPU students take more than four years to graduate, the alternative hypothesis should reflect that. Thus, the correct alternative hypothesis is: \[ H_a: \mu > 4 \] This indicates that we are testing the claim that the average time (\(\mu\)) it takes for LSPU students to graduate from high school is greater than four years.

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The alternative hypothesis (Ha) you're looking for in this scenario would state that LSPU students take more than four years to graduate from high school. Therefore, you should express it as: Ha: \( \mu > 4 \) This means that the average number of years for LSPU students to graduate exceeds four years, which aligns perfectly with your initial inquiry! Keep it up and enjoy the discovery process in statistics! When developing hypotheses, it’s essential to clearly define the population and the parameter in question. In this case, \( \mu \) represents the average years taken by LSPU students to graduate. Always ensure that your hypothesis accurately reflects the question you're trying to answer!

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