A6 P1#
Suppose we are sampling 58 observations from a normally distributed population where it is known that \(\sigma\) = 24, but \(\mu\) is unknown. We wish to test \(H_0: \mu = {{ params.mu_null }}\) against \(H_1: \mu \neq {{ params.mu_null }}\) at \(\alpha = {{ params.alpha }}\). Suppose, in reality, the null hypothesis is false and \(\mu = {{ params.mu_true }}\).
Part 1: (a)#
For the given test, please state the critical value corresponding to the left tail.
Answer Section#
Enter in a numeric value.
Part 1: (b)#
For the given test, please state the critical value corresponding to the right tail.
Answer Section#
Enter in a numeric value.
Part 2: (a)#
For what values of \(\bar{X}\) would the null hypothesis be rejected? Please provide the lower bound of this range.
Answer Section#
Enter in a numeric value.
Part 2: (b)#
Now, please provide the upper bound of this range.
Answer Section#
Enter in a numeric value.
Part 3#
What is the Type I error?
Answer Section#
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Part 4#
What is the Type II error?
Answer Section#
Enter in a numeric value.
Part 5#
What is the power of the test?
Answer Section#
Enter in a numeric value.
Attribution#
Problem is licensed under the CC-BY-NC-SA 4.0 license.