We consider the differences between the reading and writing scores of a random sample of 200 students who took the High School and Beyond Survey The mean and standard deviation of the differences Xread write 0 543 and 8 878 points a Calculate a 95 confidence interval for the average difference between the reading and writing scores of all students Round your answers to two decimal places 1 77 0 69 b Interpret this interval in context Round your answers to two decimal places We are 95 confident that on the reading test students score on average points lower to 0 7 c Does the confidence interval provide convincing evidence that there is a real difference in the average scores Explain Since 0 is included in the interval the confidence interval does not points higher than they do on the writing test provide convincing evidence that there is a real difference in the average scores