Question

question 5
2 pts
assume that a hypothesis test of the given claim will be conducted. identify the type i or type ii error for the test.
the principal of a middle school claims that the standard deviation of the test scores of the seventh - graders at his school is less than 14.7. identify the type i error for the test.
○ fail to reject the claim that the standard deviation is equal to 14.7 when it is actually greater than 14.7.
○ fail to reject the claim that the standard deviation is equal to 14.7 when it is actually less than 14.7.
○ reject the claim that the standard deviation is equal to 14.7 when it is actually 14.7.
○ reject the claim that the standard deviation is equal to 14.7 when it is actually less than 14.7.

Explanation:

First, define the hypotheses: The null hypothesis \(H_0\) is the principal’s claim (\(\sigma = 14.7\)), and the alternative hypothesis \(H_a\) is the actual situation (\(\sigma < 14.7\)). Type I error is rejecting \(H_0\) when \(H_0\) is true. Here, if we reject the claim (\(H_0: \sigma = 14.7\)) but the actual standard deviation is equal to 14.7 (so \(H_0\) is true), this matches the definition of Type I error.

Answer:

Reject the claim that the standard deviation is equal to 14.7 when it is actually 14.7.