# 5.22 High School and beyond, Part II: We considered the differences between the reading andwriting scores of a random sample of 200 students who took the High School and Beyond Survey inExercise 5.21. The mean and standard deviation of the differences are Dead-write = -0.545 and8.887 points respectively.(a) Calculate a 95% confidence interval for the average difference between the reading and writingscores of all studentspoints (please round to two decimal places)points (please round to two decimal places)lower bound:upper bound:(b) Interpret this interval in context.95% of students will have a difference between reading and writing scores that falls withinour confidence intervalWe can be 95% confident that our confidence interval contains the mean differencebetween reading and writing scores of these 200 studentsWe can be 95% confident that the average difference between reading and writing scoresof all students is contained within our confidence interval(c) Does the confidence interval provide convincing evidence that there is a real difference in theaverage scores? Explain.no, since 0 is contained in our confidence intervalyes, since 0 is contained in our confidence intervalyes, because negative scores are impossible and our confidence interval contains themno, because or confidence interval contains both positive and negative values

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Introduction:

The 100 (1 – α) % confidence interval for the population mean difference, μd, for given sample standard deviation of differences, sd in case of paired samples is: (x̅d – (/2; n – 1­) (sd /√n), x̅d + (/2; n – 1) (sd /√n)).

Here, n is the sample size, x̅d is the sample mean difference, and /2; n – 1 is the critical...

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