Answer Happy

Susan is interested in whether the age at which students study with the OU is different depending on where the students live. She analyses the data for the 544 students who started studying M248 in October 2020 and finds that 69 of these were from Scotland and 29 them were from Wales. The Scottish students had a mean age of 41.6 years with a standard deviation of 13.8. Whereas the Welsh students had mean age of 36.8 with a standard deviation of 10.9.
(d) Assume that the two populations of OU Scottish and Welsh students have normal distributions with a common variance. Calculate by hand the pooled estimate of the common standard deviation.
(e) Susan uses Minitab to calculate a 95% two-sample t-interval, with a pooled variance, for the difference between the mean ages of Scottish and Welsh students. The interval she calculates is (-0.92, 10.52). Based on this t-interval what is your conclusion, and why, about the mean ages of Scottish and Welsh students?