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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? \( \mu<90 \) \( \mu>90 \) \( \mu=90 \) \( \mu \neq 90 \) DONE

Ask by Sanders Sullivan. in the United States
Feb 25,2025

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

Solution

In hypothesis testing, the alternative hypothesis \( H_a \) represents what we are trying to find evidence for, while the null hypothesis \( H_0 \) represents a statement of no effect or no difference. Given that the average high temperature in Oklahoma City is believed to be \( 92^{\circ} \mathrm{F} \), we can set up the hypotheses as follows: 1. **Null Hypothesis \( H_0 \)**: The average high temperature is \( 90^{\circ} \mathrm{F} \) (or any value that we are testing against). - \( H_0: \mu = 90 \) 2. **Alternative Hypothesis \( H_a \)**: This is what we are testing for. Since we are interested in whether the average high temperature is different from \( 90^{\circ} \mathrm{F} \), the alternative hypothesis would be: - \( H_a: \mu \neq 90 \) Thus, the correct alternative hypothesis for this situation is: \( H_a: \mu \neq 90 \)

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If your sample data suggests that the average high temperature in Oklahoma City is 92°F, the alternative hypothesis, \( H_{a} \), would be \( \mu \neq 90 \). This hypothesis indicates that the average high temperature is not equal to 90°F, which is the value you might be testing against. Essentially, you're asserting that the true average temperature differs from 90°F, possibly being higher based on your observation. In hypothesis testing, it's crucial to differentiate between the null hypothesis, which often posits that there's no difference (in this case, that the average is 90°F), and the alternative hypothesis, which suggests a difference exists. So, you’re on the correct track in thinking there's a need for exploration beyond that single number!

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