Question

A recent study investigated tractor skidding distances along a road in a forest. The skidding distances​ (in meters) were measured at 20 randomly selected road sites. The data are given in the accompanying table. A logger working on the road claims that the mean skidding distance is at least 425 meters. Is there sufficient evidence to refute this​ claim? Use α=0.05.

500	359	465	201	292	414	438	586	430	532
380	300	183	257	281	397	302	316	140	438

State the hypotheses to test the claim that the mean skidding distance is at least 425

meters. Choose the correct answer below.

A. H0​: μ ≠ 425

Ha​ :μ = 425

B. H0​: μ= 425

Ha​: μ ≠ 425

C.H0​:μ = 425

Ha​:μ > 425

D.H0​:μ =4 25

Ha​:μ < 425

Answer 1

Data:    

n = 20   

μ = 425   

s = 118.86   

x-bar = 360.55   

Hypotheses:    

Ho: μ ≥ 425   

Ha: μ < 425   

Decision Rule:    

α = 0.05   

Degrees of freedom = 20 - 1 = 19

Critical t- score = -1.729132792   

Reject Ho if t < -1.729132792   

Test Statistic:    

SE = s/√n = 118.86/√20 = 26.57790398

t = (x-bar - μ)/SE = (360.55 - 425)/26.5779039805625 = -2.424946679

p- value = 0.012723698   

Decision (in terms of the hypotheses):    

Since -2.424946679 < -1.729132792 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is enough evidence that the mean skidding distance is less than 425 m. The claim can be refuted.