A study published in Applied Psycholinguistics (June 1998 compared the language skills of young children (16-30 months old) from low income and middle income families. Suppose each child in a random sample of 25 low-income children was administered the Communicative Development Inventory (CDI) exam. The sample sentence complexity scores had a mean of 7.62 and a standard deviation of 9. Assume the scores for low-income children are normally distributed.

a. Calculate a 99% confidence interval for the mean sentence complexity score for low-income children. Show your work. Check the conditions first.

b. Interpret the confidence interval in the context of the problem.

c. Suppose we know that the true mean sentence complexity score of middle-income children is 15.55. Is there evidence that the true mean for low-income children differs from 15.55? Use your answers to the previous parts to justify your answer.