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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Asked Nov 18, 2019
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5.22 High School and beyond, Part II: 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 5.21. The mean and standard deviation of the differences are Dead-write = -0.545 and
8.887 points respectively.
(a) Calculate a 95% confidence interval for the average difference between the reading and writing
scores of all students
points (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 within
our confidence interval
We can be 95% confident that our confidence interval contains the mean difference
between reading and writing scores of these 200 students
We can be 95% confident that the average difference between reading and writing scores
of all students is contained within our confidence interval
(c) Does the confidence interval provide convincing evidence that there is a real difference in the
average scores? Explain.
no, since 0 is contained in our confidence interval
yes, since 0 is contained in our confidence interval
yes, because negative scores are impossible and our confidence interval contains them
no, because or confidence interval contains both positive and negative values
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5.22 High School and beyond, Part II: 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 5.21. The mean and standard deviation of the differences are Dead-write = -0.545 and 8.887 points respectively. (a) Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students points (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 within our confidence interval We can be 95% confident that our confidence interval contains the mean difference between reading and writing scores of these 200 students We can be 95% confident that the average difference between reading and writing scores of all students is contained within our confidence interval (c) Does the confidence interval provide convincing evidence that there is a real difference in the average scores? Explain. no, since 0 is contained in our confidence interval yes, since 0 is contained in our confidence interval yes, because negative scores are impossible and our confidence interval contains them no, 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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