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 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 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.

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

Answer 1

The statistical software output for this problem is:

Hence,

a) 95% confidence interval:

Lower limit = -1.78

Upper limit = 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. Option C is correct.

c) No, since 0 is contained in our confidence interval. Option A is correct.