Q&A Bank 3.27

[Anjum]

An office manager wants to analyse the variability in the time taken for her typists to
complete a given task. She has given seven typists the task and the results are as
follows (in minutes):
15, 17.2, 13.7, 11.2, 18, 15.1, 14
The manager wants a 95% confidence interval for the true standard deviation of time
taken of the form s > k . Calculate the value of k .

As per the solution it is given



doubt is since we want 95% confidence interval for s>k so we need to find only the lower limit of s and should have thus taken chisquare at 0.95 level as (0.975, df) gives the lower value for a 95% confidence interval for s>k then why are we taking chisquare value at 0.05 level.

 

[Bharti Singla]

Hi
I guess this is one-sided confidence interval i.e. (k,∞). Means the whole 5% area will be in left in this case. When finding 95% CI using two-sided CI, the 5% region is divided among both sides each of 2.5%. But in this case, the whole region of 5% will be in left side and the upper limit will be ∞. See the graph below, it may help.