The relationship between confidence intervals and hypothesis testing 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 salmon fillets per night than the restaurant located on the north side of the city. the statistician selects a random sample of size n_1 = 35 nights that the south side restaurant is open. for each night in the sample, she collects data on the number of salmon fillets sold at the south side location and computes the sample mean m_1 = 34.81 and the sample variance s_1^2 = 28. likewise, she selects a random of size n_2 = 32 nights that the north side restaurant is open. for each night in the sample, she collects data on the number of salmon fillets sold at the north side location and computes the sample mean m_2 = 39.26 and the sample variance s_2^2 = 27. 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 salmon fillets sold per night at the south side restaurant and the mean number of salmon fillets sold per night at the north side restaurant. this 95% confidence interval is-4.45 plusminus 2.5624 salmon fillets. if she were to formulate null and alternative hypotheses as h_0: mu_1 - mu_2 = 0, h_1: mu_1 - mu_2 notequalto 0 and conduct a hypothesis test with alpha = 0.5, she would conclude that between the two restaurants a significant difference between the mean nightly sales of salmon fillets between the two restaurants.