7. Sampling Distributions & Confidence Intervals: Mean
Introduction to Confidence Intervals
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Find for a 90% confidence interval.
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Understand that the confidence level is the probability that the interval contains the true parameter value. For a 90% confidence interval, this means we are 90% confident that the interval contains the true parameter.
Recognize that the confidence level is related to the significance level, denoted as \( \alpha \). The significance level is the probability of rejecting the null hypothesis when it is true, which is the complement of the confidence level.
Calculate \( \alpha \) by subtracting the confidence level from 1. For a 90% confidence interval, \( \alpha = 1 - 0.90 \).
Perform the subtraction: \( \alpha = 0.10 \). This means that the significance level for a 90% confidence interval is 0.10.
Conclude that \( \alpha = 0.10 \) is the correct significance level for a 90% confidence interval, which corresponds to the probability of making a Type I error.
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