Question

In: Statistics and Probability

Test runs for the operating time before overeating of 9 randomly selected motors of a certain...

Test runs for the operating time before overeating of 9 randomly selected motors of a certain type showed a sample mean of 39.7 hours and a sample standard deviation of 2.5 hours. Find a 95% confidence interval for the standard deviation of the length of time a motor of this type will operate before overheating.

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Expert Solution

We have given here,                                              
                                              
                                  
Sample standard deviation=2.5 hours   
Sample size =9                                      
                                              
Degree of freedom =n-1=   8                                  
Level of significance given =1-0.95=0.05                                  
Chi square critical value for lower tail=2.18                          
                                              
Chi square critical value for upper tail=17.535                              
                                              
We can use here confidence interval formula for population standard deviation


=(1.69,4.79)
                                              
                                              
                                              
                                              
                      
                                              
Lower confidence limit for population standard deviation=1.69 hours
                                              
Upper confidence limit for Population standard deviation=4.79 hours


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