Textbook Question
The area under the t-distribution with 18 degrees of freedom to the right of t = 1.56 is 0.0681. What is the area under the t-distribution with 18 degrees of freedom to the left of t = –1.56? Why?
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7. Sampling Distributions & Confidence Intervals: Mean
Introduction to Confidence Intervals
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
In the context of hypothesis testing, which of the following gives the probability of making a Type I error?
A
The significance level
B
The power of the test
C
The confidence level
D
The p-value
Verified step by step guidance1
Understand the definition of a Type I error: it occurs when we reject the null hypothesis \( H_0 \) even though it is actually true.
Recall that the probability of making a Type I error is denoted by the significance level, commonly represented as \( \alpha \).
Recognize that the significance level \( \alpha \) is set by the researcher before conducting the test and represents the threshold for rejecting \( H_0 \).
Differentiate this from the power of the test, which is \( 1 - \beta \), where \( \beta \) is the probability of a Type II error (failing to reject \( H_0 \) when it is false).
Note that the confidence level \( 1 - \alpha \) represents the probability of not making a Type I error, and the p-value is the observed probability used to decide whether to reject \( H_0 \), but it is not the probability of a Type I error itself.
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