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 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.
(c) Does the confidence interval provide convincing evidence that
there is a real difference in the average scores? Explain.
The statistical software output for this problem is:
Hence,
a) 95% confidence interval will be:
Lower bound = -1.78
Upper bound = 0.69
b) We can be 95% confident that the average difference between reading and writing scores of all students is contained within our confidence interval.
c) No, since 0 is contained in our confidence interval
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