Question

A collegiate long jumper is hoping to improve his distance with improved conditioning. His new conditioning routine should help him be able to jump further than he has in the past. Before the conditioning began, the jumper was averaging 24.5 feet. After his new routine was finished, he jumps a series of 30 jumps over the course of a week. A histogram of this sample data from the 30 jumps is approximately normal with an average of 25.0 feet and a standard deviation of 1.6 feet. Describe, in context, what the results would be of a Type 1 error and a Type 2 error from this conclusion?

Answer 1

Type -I error :

If type-I error occur in above case which means we are rejecting the null hypothesis though it is true. Means the average of the length of jumpers jump is actually 24.5 but still we reject it and conclude that average is greater than 24.5.

Type-II error:

Type -II error ocure in above case means we are accepting null hypothesis though it is false. Means the actual average of length of jumpers jump is greater than 24.5 but we reject it and conclude that average is equals to 24.5.