As a construction engineer for a city, you are responsible for ensuring that the company that is providing gravel for a new road puts as much gravel in each truckload as they claim to. It has been estimated that it will take 500 truckloads of gravel to complete this road, so you plan to measure the volume of gravel in an SRS of 25 trucks to make sure that the company isn't delivering less gravel per truckload than they claim. Each truckload is supposed to have 20 m3of gravel, so you will test the hypothesis H0: μ = 20 versus Ha: μ < 20.
Describe what a Type I error is in this context.
- We find evidence that the company has been delivering less gravel than they claim, even though they have actually been doing everything correctly.
- We find evidence that the company has been delivering less gravel than they claim, and successfully catch them violating their contract.
- Our test results are inconclusive.
- We fail to reject the company's claim, even though they have been delivering less than 20 cubic meters per truckload.
- We fail to reject the company's claim, and they have been doing everything correctly.