객관식
For the standard normal distribution, what is the probability that ? Choose the closest value.
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6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
객관식
For a two-tailed hypothesis test at the significance level using the standard normal distribution, what are the critical value(s) for ?
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검증된 단계별 안내1
Identify that the problem involves a two-tailed hypothesis test at the 5% significance level, which means the total area in both tails of the standard normal distribution is 0.05.
Since the test is two-tailed, split the significance level equally between the two tails: each tail will have an area of 0.025 (i.e., 0.05 / 2).
Use the standard normal distribution table (Z-table) or a statistical software to find the z-value that corresponds to the cumulative probability of 0.025 in the lower tail and 0.975 in the upper tail.
The critical values are the z-scores that mark the boundaries of the rejection regions: one negative z-value for the lower tail and one positive z-value for the upper tail.
Express the critical values as \(-z_{\alpha/2}\) and \(z_{\alpha/2}\), where \(\alpha = 0.05\), so the critical values are \(-z_{0.025}\) and \(z_{0.025}\).
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