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. Construct a 95% Confidence Interval for the situation in the problem above. Use it to address the issue of Practical versus Statistical significance.

Answer 1

t critical value at 0.05 level with 29 df = 2.045

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

25 - 2.045 * 1.6 / sqrt(30) < < 25 + 2.045 * 1.6 / sqrt(30)

24.40 < < 25.60

95% CI is ( 24.40 , 25.60 )

Since claimed mean 24.5 contains in confidence interval, we do not have sufficient evidence to

support the claim that jumper improve his distance with improved conditioning.