Question

**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 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
- 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.

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

Answer #1

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

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...

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