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 x̄read-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. ( )We can be 95% confident that the average difference between reading and writing scores of all students is contained 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 ( )95% of students will have a difference between reading and writing scores that falls within our confidence interval (c) Does the confidence interval provide convincing evidence that there is a real difference in the average scores? Explain. ( )no, because or confidence interval contains both positive and negative values ( )yes, since 0 is contained in our confidence interval ( )yes, because negative scores are impossible and our confidence interval contains them ( )no, since 0 is contained in our confidence interval

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 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.

( )We can be 95% confident that the average difference between reading and writing scores of all students is contained 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
( )95% of students will have a difference between reading and writing scores that falls within our confidence interval

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

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

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The 100 (1 – α) % confidence interval formula for the population mean difference between two paired sets of observations when population standard deviation is not known, is defined as follows:

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