3. The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below 20 10 20 Diferences in scores (read - write) a. Is there a clear difference in the average reading and witing scores? b. Are the reading and writing scores of each student independent of each other? The average observed difference in scores is xd=-0.545x¯d=-0.545, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams? Conduct a hypothesis test; interpret your conclusions in context.

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3. The National Center of Education Statistics conducted a survey of high school seniors,
collecting test data on reading, writing, and several other subjects. Here we examine a
simple random sample of 200 students from this survey. Side-by-side box plots of reading
and writing scores as well as a histogram of the differences in scores are shown below
40
30
60
20-
10
-20
10
20
read
write
Differences in scores (read - write)
a. Is there a clear difference in the average reading and writing scores?
b. Are the reading and writing scores of each student independent of each other? The
average observed difference in scores is xd=-0.545x d=-0.545, and the standard
deviation of the differences is 8.887 points. Do these data provide convincing evidence of
a difference between the average scores on the two exams? Conduct a hypothesis test;
interpret your conclusions in context.
c. Based on the results of this hypothesis test, would you expect a confidence interval for
the average difference between the reading and writing scores to include 0? Explain your
reasoning.
d. Calculate a 95% confidence interval for the average difference between the reading and
writing scores of all students.
e. Interpret this interval in context.
f. Does the confidence interval provide convincing evidence that there is a real difference in
the average scores? Explain
scores
Transcribed Image Text:3. The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below 40 30 60 20- 10 -20 10 20 read write Differences in scores (read - write) a. Is there a clear difference in the average reading and writing scores? b. Are the reading and writing scores of each student independent of each other? The average observed difference in scores is xd=-0.545x d=-0.545, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams? Conduct a hypothesis test; interpret your conclusions in context. c. Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the reading and writing scores to include 0? Explain your reasoning. d. Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. e. Interpret this interval in context. f. Does the confidence interval provide convincing evidence that there is a real difference in the average scores? Explain scores
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