a hospital spokesperson states that 2% of emergency rooms visits by college undergraduates are for alcohol related health problems

Question

Mathematics

Katelyn Rivas

4 January, 11:19

a hospital spokesperson states that 2% of emergency rooms visits by college undergraduates are for alcohol related health problems

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Answers (1)

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Leroy Cooke · Answer 1

Type I error: Reject H₀: p = 0.02 when in fact p = 0.02.

Type II error: Fail to Reject H₀: p = 0.02 when in fact p ≠ 0.02.

Step-by-step explanation:

The complete question is:

Write a sentence describing the type I and type II errors for the hypothesis test for the indicated claim.

"A hospital spokesperson states that 2% of emergency rooms visits by college undergraduates are for alcohol related health problems."

Solution:

A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

The claim made by the hospital spokesperson is, 2% of emergency rooms visits by college undergraduates are for alcohol related health problems.

The hypothesis can be defined as:

H₀: The proportion of emergency rooms visits by college undergraduates for alcohol related health problems is 2%, i. e. p = 0.02.

Hₐ: The proportion of emergency rooms visits by college undergraduates for alcohol related health problems is not 2%, i. e. p ≠ 0.02.

A type I error will be committed when we conclude that the null hypothesis can be rejected, i. e. proportion of emergency rooms visits by college undergraduates for alcohol related health problems is not 2%, when in fact we are rejecting a true null hypothesis, i. e. the proportion is 2%.

A type II error will be committed when we conclude that the null hypothesis cannot be rejected, i. e. proportion of emergency rooms visits by college undergraduates for alcohol related health problems is 2%, when in fact we are failing to reject a true null hypothesis, i. e. the proportion is not 2%.