The brothers Odd and Kjell Aukrust lie home in bed with whooping cough, and as Kjell rattles off a particularly long-lasting cough, Odd exclaims: That one lasted for rather a long time, but not as long as mine do! Kjell disagrees, so they decide to measure coughing times (in seconds):

- Odd: 22, 20, 21, 20, 21, 21, 19, 21

- Kjell: \(15,12,32,12,11,13,14\).

The budding statistician Odd assumes the lengths of the coughing bouts follow Normal distributions, respectively \(\phi_{\left(\mu_{K}, \sigma_{K}ight)}\) (Kjell) and \(\phi_{\left(\mu_{O}, \sigma_{O}ight)}\) (Odd). He would like to establish with significance \(\alpha=0.2\) that his own bouts of coughing last longer than Kjell's, in other words he wants to test \(H_{1}: \mu_{O}>\mu_{K}\). But Odd is ill today, so he leaves it up to us to do the work. We use neutral priors.