Question

Listed below are speeds​ (mi/h) measured from traffic on a busy highway. This simple random sample was obtained at​ 3:30 P.M. on a weekday. Use the sample data to construct a 98​% confidence interval estimate of the population standard deviation. 60 65 65 55 65 55 59 58 59 69 62 66.
The confidence interval estimate is ____ ​mi/hless thansigmaless than _____ ​mi/h. ​(Round to one decimal place as​ needed.)

Answer 1

We have for given data,                                      
                                      
Sample variance =20.4545                              
Sample standard deviation=4.523                      
Sample size =12                              
                                      
Degree of freedom =n-1=   11                          
Level of significance given =0.02                          
Chi square critical value for lower tail=3.053                      
                                      
Chi square critical value for upper tail=24.725                      
                                      
                                  
We can use here confidence interval formula for population standard deviation                                      

(n-1) S2 (n-1).S2 V X1-a/2) V Xa/2)

(12 - 1) * 20.4545 24.725 (12 - 1) * 20.4545 3.053

=(3.0,8.6)

The confidence interval estimate is 3.0 ​mi/h < $\sigma<$ 8.6 ​mi/h.