Question

Suppose the null hypothesis, h0, is a weightlifting bar that can withstand weights of 800 pounds and less. and the alternative hypothesis, ha, is a weightlifting bar that can withstand weights of greater than 800 pounds. What is the type I error in this scenario?

1) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of greater than 800 pounds.
2) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds.
3) You conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds.
4) You conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of greater than 800 pounds.

Answer 1

A Type I error in the given scenario is concluding that the weightlifting bar can withstand weights greater than 800 pounds when it can only withstand up to 800 pounds.

Step-by-step explanation:

In hypothesis testing, a Type I error occurs when the null hypothesis (H0) is incorrectly rejected when it is actually true. In the scenario where the null hypothesis is that a weightlifting bar can withstand weights of 800 pounds and less, and the alternative hypothesis is that it can withstand weights greater than 800 pounds, a Type I error would be to conclude that the bar can actually withstand more than 800 pounds when it cannot — in other words, falsely believing the bar is stronger than it truly is. The correct choice matching this definition is option 3: You conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds.