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Question
Math
Posted 10 months ago

A city planner will consider adding electric vehicle charging stations if she is convinced that more than 15%15 \% of residents would use them. She will survey a sample of residents to test the hypotheses H0:p15%H_{0}: p \leq 15 \% vs. Ha:p>15%H_{\mathrm{a}}: p>15 \%, where pp is the true proportion of residents that would use the stations.

Suppose that H0H_{0} is actually true.
Which situation below would have the lowest probability of a Type I error?

Choose 1 answer:
(A) n=200n=200 and α=0.01\alpha=0.01
(B) n=200n=200 and α=0.05\alpha=0.05
(C) n=300n=300 and α=0.10\alpha=0.10
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Answer from Sia
Posted 10 months ago
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 α\alpha
step 3
Compare the given significance levels α\alpha for each option to determine which has the lowest value
step 4
Note that the sample size nn does not affect the probability of a Type I error when the null hypothesis is true
step 5
Conclude that the option with the lowest significance level α\alpha will have the lowest probability of a Type I error
[1] Answer
(A) n=200n=200 and α=0.01\alpha=0.01
Key Concept
Type I Error Probability
Explanation
The probability of a Type I error in hypothesis testing is determined by the significance level α\alpha, not by the sample size nn. The option with the lowest α\alpha has the lowest probability of committing a Type I error.

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