IMathAS-libretexts

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 x̄_read-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.
lower bound: points (please round to two decimal places)
upper bound: points (please round to two decimal places)

(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, because negative scores are impossible and our confidence interval contains them
yes, since 0 is contained in our confidence interval
no, because or confidence interval contains both positive and negative values

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