A city planner will consider adding electric vehicle charging stations if she is convinced that more than $15 \%$ of residents would use them. She will survey a sample of residents to test the hypotheses $H_{0}: p \leq 15 \%$ vs. $H_{\mathrm{a}}: p15 \%$, where $p$ is the true proportion of residents that would use the stations.

Suppose that $H_{0}$ is actually true.
Which situation below would have the lowest probability of a Type I error?

Choose 1 answer:
(A) $n=200$ and $\alpha=0.01$
(B) $n=200$ and $\alpha=0.05$
(c) $n=300$ and $\alpha=0.10$

Question

A city planner will consider adding electric vehicle charging stations if she is convinced that more than $15 \%$ of residents would use them. She will survey a sample of residents to test the hypotheses $H_{0}: p \leq 15 \%$ vs. $H_{\mathrm{a}}: p>15 \%$, where $p$ is the true proportion of residents that would use the stations.

Suppose that $H_{0}$ is actually true.
Which situation below would have the lowest probability of a Type I error?

Choose 1 answer:
(A) $n=200$ and $\alpha=0.01$
(B) $n=200$ and $\alpha=0.05$
(c) $n=300$ and $\alpha=0.10$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the definition of a Type I error in hypothesis testing. ‖ ‖ step 2 ⋮ Recognize that the probability of a Type I error is denoted by the significance level $\alpha$. ‖ ‖ step 3 ⋮ Compare the given significance levels $\alpha$ for each option to determine which has the lowest value. ‖ ‖ step 4 ⋮ Conclude that the option with the lowest significance level $\alpha$ will have the lowest probability of a Type I error. ‖ ∻1 Answer∻ ⚹ (A) $n=200$ and $\alpha=0.01$ ⚹ ∻Key Concept∻ ⚹Type I Error Probability⚹ ∻Explanation∻ ⚹The probability of a Type I error in hypothesis testing is equal to the significance level $\alpha$. The lower the $\alpha$, the lower the probability of committing a Type I error.◊What is the formula for calculating the probability of a Type I error in hypothesis testing scenarios?⍭ Generate me a similar question◊⚹

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