Suppose that a sports team\'s management will approve a new uniform design if ov

Question

Suppose that a sports team's management will approve a new uniform design if over 70% of the fans approve of the new design. A hypothesis test is conducted using data gathered via a SRS of the team's fans, with In the context of the above problem, what would the specified statement of conclusion be if a Type I Error was made in the hypothesis test? In the context of the above problem, what would the specific true population nature and specific statement of conclusion be if a Type 11 Error was made in the hypothesis test?

Explanation / Answer

a)

A type I error is incorrectly rejecting a true null hypothesis.

Hence, it is concluding that the true population proportion of the fans who approve the new design is greater than 0.70, when in fact, it is just 0.70.

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b)

A type II error is incorrectly failing to reject a false null hypothesis.

Hence, it is concluding that the true population proportion of the fans who approve the new design is equal to 0.70, when in fact, it is greater than 0.70.

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