Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective homebuyers in the Middletown and Brockton areas of the city. One item of interest is the number of years children remain in the same district for schooling. A sample of 40 households with school-aged children in Middletown was randomly selected. The mean length of time in the district was 7.6 years, with a standard deviation of 2.3 years.
A sample of 55 households in Brockton revealed the mean length of time in the district was 8.1 years, with a standard deviation of 2.9 years. At the .05 level of significance, can we conclude the Middletown students stayed in their districts less time than the Brockton students? Use the five-step hypothesis testing procedure.