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A senator is thinking about running for president. But she will only do so if more than \( 60 \% \) of the voters view her favorably. She gathers some data to see if she has this level of support. Which statistical method would be best for her to use? O Hypothesis test Regression analysis Binomial distribution Confidence interval

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

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A hypothesis test is the best method for her to determine if her support exceeds 60%.

Solución

The best method for her situation is a hypothesis test. She wants to know if her level of support is greater than 60 percent based on her data sample. By setting up a hypothesis test (for example, with null hypothesis H₀: p ≤ 0.60 and alternative hypothesis H₁: p > 0.60), she can statistically assess whether her true level of support exceeds 60 percent. Regression analysis is more suited for situations where you need to examine the relationship between variables, and the binomial distribution might underlie the test but isn’t the main method. While a confidence interval could give her an estimation of support, a hypothesis test directly addresses whether the support is significantly greater than 60 percent for making her decision.

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Bonus Knowledge

To determine if more than \( 60\% \) of voters view her favorably, the senator should use a hypothesis test. Specifically, she can set up a null hypothesis stating that \( 60\% \) or fewer voters view her favorably, and an alternative hypothesis claiming that more than \( 60\% \) do. This method allows her to analyze her sample data to see if there is sufficient evidence to reject the null hypothesis in favor of her presidential run. A confidence interval could also provide valuable insight. By constructing a confidence interval for the proportion of voters who view her favorably, she can estimate the range within which the true percentage likely falls. If the lower bound of this confidence interval exceeds \( 60\% \), it adds more support for her potential candidacy.

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