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You have sample data that leads you to believe that the average high temperature in Oklahoma City is \( 92^{\circ} \mathrm{F} \). What is the alternative hypothesis, \( H_{a} \), for this situation? \( \mu<90 \) \( \mu>90 \) \( \mu=90 \) \( \mu \neq 90 \)

Ask by West Bernard. in the United States
Feb 27,2025

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The alternative hypothesis \( H_a \) is \( \mu \neq 90 \).

Solution

In hypothesis testing, the alternative hypothesis \( H_a \) represents a statement that contradicts the null hypothesis \( H_0 \). In this case, the null hypothesis would typically state that the average high temperature in Oklahoma City is equal to a specific value, which we can assume to be \( 90^{\circ} \mathrm{F} \) based on the options provided. Given that the average high temperature is believed to be \( 92^{\circ} \mathrm{F} \), the alternative hypothesis would suggest that the average temperature is not equal to \( 90^{\circ} \mathrm{F} \). Thus, the correct alternative hypothesis \( H_a \) for this situation is: \[ H_a: \mu \neq 90 \] This indicates that the average high temperature is significantly different from \( 90^{\circ} \mathrm{F} \).

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The Deep Dive

In this situation, the alternative hypothesis \( H_{a} \) would be \( \mu \neq 90 \). This implies that you are testing whether the average high temperature in Oklahoma City is not equal to 90°F, indicating you are considering both possibilities—higher than or lower than 90°F. It's a way of saying, "Hey, let's see if our findings really stand out compared to this benchmark!" To add a little more fun to the mix, think of hypothesis testing like a courtroom drama! The null hypothesis \( H_{0} \) is like the defendant, assumed innocent until proven guilty, while the alternative hypothesis \( H_{a} \) is the prosecution, trying to prove that the average temperature has an intriguing story of its own—challenging the status quo!

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