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

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Part 1: (b)

For the given test, please state the critical value corresponding to the right tail.

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Part 2: (a)

For what values of \(\bar{X}\) would the null hypothesis be rejected? Please provide the lower bound of this range.

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Part 2: (b)

Now, please provide the upper bound of this range.

Answer Section

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Part 3

What is the Type I error?

Answer Section

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Part 4

What is the Type II error?

Answer Section

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Part 5

What is the power of the test?

Answer Section

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Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.