Question

TRACTOR SKIDDING CONFIDENCE INTERVAL Forest engineers are interested in studying the skidding distances of tractors along a new road in a European Forest. The engineers collect data on a random sample of 12 tractors. The collected data (in meters) are: 350, 285, 574, 439, 295, 184, 261, 273, 400, 311, 141, 425. The standard deviation for this random sample is 118.46. (Source: A First Course in Statistics, McClave & Sincich, 10th Edition) Which statement below is the correct interpretation of the confidence interval? Enter 1,2,3, or 4 in the box. I am 95% confident that the average skidding distance, xbar, is significantly greater than suspected. I am 95% confident that the average skidding distance, µ, is significantly greater than suspected. I am 95% confident that the average skidding distance, µ, is between 252.9 ft. and 403.4 ft. I am 95% confident that the average skidding distance, xbar, is between 252.9 ft. and 403.4 ft.

Answer 1

We have for given data,      
          
Sample mean =328.17  
Sample standard deviation =118.46
Sample size =12  
Level of significance=   1-0.95=   0.05  
Degree of freedom =11  
          
t critical value is (by using t table)=   2.201  
          
Confidence interval formula is

=(252.90,403.4)          
          
          
          
Lower confidence limit=252.9  
          
Upper confidence limit=403.4  

Option 3) is correct.

I am 95% confident that the average skidding distance, µ, is between 252.9 ft. and 403.4 ft.