In an effort to better manage his inventory levels, the owner of two steak and seafood restaurants, both located in the same city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the south side sells more prime rib steaks per night than the restaurant located on the north side of the city.

The statistician selects a random sample of size n1=38 nights that the south side restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the south side location and computes the sample mean M1=12.98 and the sample variance s2/1 =33. Likewise, she selects a random sample of size n2=42 nights that the north side restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the north side location and computes the sample mean M2=18.58 and the sample variance s2/2=28.

The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 95% confidence interval for estimating the difference between the mean number of prime rib steaks sold per night at the south side restaurant and the mean number of prime rib steaks sold per night at the north side restaurant. This 95% confidence interval is -5.6 + or - 2.4566 prime rib steaks.

If she were to formulate null and alternative hypotheses as H0: u1-u2=0, H1:u1-u2does not equal 0 and conduct a hypothesis test with a=.05, the null hypothesis rejected based on the result that a difference of zero -in the computed interval. Hence, she would conclude that there a significant difference between the mean nightly sales of prime rib steaks between the two restaurants.