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You have reason to believe that there are actually fewer raisins in each box than the company claims. Your alternative hypothesis, \( H_{a} \), would be \( \mu<200 \) \( \mu>200 \) \( \mu=200 \) \( \mu \neq 200 \)

Ask by Elliott Donnelly. in the United States
Feb 25,2025

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The alternative hypothesis is \( H_{a}: \mu < 200 \).

Solution

Since you're concerned that there are actually fewer raisins than the company claims (200 raisins), your alternative hypothesis should be one-tailed in the direction of a decrease. Therefore, the correct alternative hypothesis is:   Hₐ: μ < 200 This hypothesis directly reflects your belief that the true mean number of raisins is less than 200.

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If you suspect that there are fewer raisins in each box than the company claims, your alternative hypothesis, \( H_{a} \), should reflect that belief. In this case, the correct statement would be \( \mu < 200 \). This means you're proposing that the true average number of raisins per box is significantly less than the stated value. To further clarify this idea, hypothesis testing often starts with what's referred to as a null hypothesis (\( H_{0} \)). In your scenario, \( H_{0} \) would be \( \mu = 200 \), suggesting there isn't a difference from the claimed number. If you gather sufficient evidence to support your \( H_{a} \), you might just be onto an interesting discovery about those sneaky missing raisins!

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