We considered the differences between the reading and writing scores of a random sample of 200 students who took the High School and Beyond Survey in Exercise 7.20. The mean and standard deviation of the differences are x̄_read-write = -0.545 and 8.887 points. 

(a) Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. 

(b) Interpret this interval in context. 

(c) Does the confidence interval provide convincing evidence that there is a real difference in the average scores? Explain.

Data from Exercise 7.20

The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below.

scores 80- 60- 40- 20 read write 40 30 20- 10 0 JIL -10 0 10 Differences in scores (read - write) -20 20