Question: In each experiment, determine whether the data are obtained independently or are paired. If the data are independent, indicate the two distinct populations. If the data are paired, indicate the common characteristic.
a. School board members believe adding a teacher's aide to each K-4 class will improve classroom management and increase instruction time. Twenty-six elementary classrooms are selected at random, and the daily instruction time for each is recorded. A teacher's aide is then added to each classroom, and the daily instruction time is recorded again. The data will be used to determine whether there is any evidence that adding a teacher's aide increases the mean daily instruction time.
b. A researcher investigating home-insurance costs obtained a random sample of homes in the Northeast and another random sample of homes in the South. The yearly insurance cost for each home was recorded. The data will be used to determine whether there is any difference in the mean yearly home-insurance costs between the Northeast and the South.
c. Officials at the transit authority of a large city would like to compare the route times during the morning and evening rush hours. Eleven routes are selected at random. A morning and an evening route completion time are recorded for each. The data will be used to determine whether the mean evening route time is less than the mean morning route time.
d. A supplementary health-insurance provider is investigating changes in claim patterns. A random sample of 32 policyholders was selected. The total amounts claimed in 2013 and in 2014 were recorded for each person. The data will be used to determine whether there is any evidence that the mean amount claimed has increased from 2013 to 2014.
e. Random samples of 45 new home sites in Kansas and 52 new home sites in upstate New York were selected. The flatness coefficient (a unitless quantity between 0 and 1) of each lot was measured. The data will be used to determine whether the mean flatness coefficient for new home sites in Kansas is less than the mean flatness coefficient for new home sites in upstate New York.