Question

According to a report from the United States Environmental Protection Agency, burning one gallon of gasoline typically emits about 8.9 kg, of CO₂. A fuel company wants to test a new type of gasoline designed to have lower CO₂ emissions. Here are their hypotheses:

H0​​​:μ=8.9 kg

​Ha​​:μ<8.9 kg​

(where μ is the mean amount of CO₂ emitted by burning one gallon of this new gasoline).

Under which of the following conditions would the company commit a Type I error?

A - The mean amount of CO₂ emitted by the new fuel is actually 8.9 kg, and they fail to conclude it is lower than 8.9 kg
B - The mean amount of CO₂ emitted by the new fuel is actually lower than 8.9 kg, and they conclude it is lower than 8.9 kg.
C - The mean amount of CO₂ emitted by the new fuel is actually 8.9 kg, and they conclude it is lower than 8.9 kg.
D - The mean amount of CO₂ emitted by the new fuel is actually lower than 8.9 kg and they fail to conclude it is lower than 8.9 kg.

Answer 1

A Type I error would occur if the company incorrectly concludes that their new fuel has lower CO2 emissions when it actually emits 8.9 kg per gallon, the same as regular gasoline. ooption C is correct answer.

Step-by-step explanation:

The company would commit a Type I error under the condition stated in option C: The mean amount of CO2 emitted by the new fuel is actually 8.9 kg, and they conclude it is lower than 8.9 kg. In statistical hypothesis testing, a Type I error occurs when the null hypothesis (H0: μ=8.9 kg) is true, but is incorrectly rejected in favor of the alternative hypothesis (Ha: μ<8.9 kg).

This means the company would be rejecting the true state of affairs (that the new gasoline actually has the same CO2 emissions as regular gasoline) and incorrectly concluding that their new product is better when it is not.