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.

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...

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 7.20. The mean and standard deviation
of the differences are and 8.887 points.
(a) Calculate a 95% confidence interval for the average
difference between the reading and writing scores of all
students.
(b) Interpret this interval in context.
(c) Does the confidence interval provide convincing evidence
that there is a real difference in the...

The Programme Monitoring and Implementation Unit in Punjab
conducted a survey of Grade 9 Students, collecting test data on
reading, writing, and several other subjects. Here we examine a
simple random sample of 250 students from this survey. a) Create
hypotheses appropriate for the following research question: is
there an evident difference in the average scores of students in
the reading and writing exam? b) The average observed difference in
scores is mean ( reading scores) – mean ( writing...

Climate change part II. We considered the differences between
the temperature reading in Jan of 1968 and 2008 at 51 locations in
the continental US in exercise 4.9 The mean and standard deviation
of the reported differences are 1.1 degrees and 4.9 degrees
Caculate a 95% CI for the average difference between the
temperature measurements between 1968 and 2008.
Interpret that this interval in context
does the CI provide convincing evidence that the temperature was
different in 2008 Interpret this...

The table provides summary statistics on highway fuel economy of
cars manufactured in 2012 (from Exercise 5.32). Use these
statistics to calculate a 98% confidence interval for the
difference between average highway mileage of manual and automatic
cars, and interpret this interval in the context of the data.
Hwy MPG, Automatic
Hwy MPG, Manual
Mean
22.92
27.88
SD
5.29
5.01
n
26
26
lower bound: mpg (please round to two decimal
places)
upper bound: mpg (please round to two decimal...

The table provides summary statistics on highway fuel economy of
cars manufactured in 2012 (from Exercise 5.32). Use these
statistics to calculate a 98% confidence interval for the
difference between average highway mileage of manual and automatic
cars, and interpret this interval in the context of the data.
Hwy
MPG, Automatic
Hwy
MPG, Manual
Mean
22.92
27.88
SD
5.29
5.01
n
26
26
lower bound: mpg (please round to two decimal
places)
upper bound: mpg (please round to two decimal
places)
Interpret...

he table provides summary statistics on highway fuel economy of
cars manufactured in 2012 (from Exercise 5.32). Use these
statistics to calculate a 98% confidence interval for the
difference between average highway mileage of manual and automatic
cars, and interpret this interval in the context of the data.
Hwy
MPG, Automatic
Hwy
MPG, Manual
Mean
22.92
27.88
SD
5.29
5.01
n
26
26
lower bound: mpg (please round to two decimal
places)
upper bound: mpg (please round to two decimal
places)
Interpret...

An education minister would like to know whether students at
Gedrassi high school on average perform better at English or at
Mathematics. Denoting by μ1 the mean score for all
Gedrassi students in a standardized English exam and μ2
the mean score for all Gedrassi students in a standardized
Mathematics exam, the minister would like to get a 95% confidence
interval estimate for the difference between the means:
μ1 - μ2.
A study was conducted where many students were given...

More than 1 million high school students took the SAT in 2000.
The average verbal score was 428 and the standard deviation was
110.
(a) Estimate the 60th percentile of the verbal SAT scores in
2000.
(b) In California, the average verbal score was 417 and the
standard deviation was 110 points. About what percent of the
California test takers did better than the national average?
(c) Estimate the difference between national and California’s
and national SAT scores. Construct a...

More than 1 million high school students took the SAT in 2000.
The average verbal score was 428 and the standard deviation was
110.
(a) Estimate the 60th percentile of the verbal SAT scores in
2000.
(b) In California, the average verbal score was 417 and the
standard deviation was 110 points. About what percent of the
California test takers did better than the national average?
(c) Estimate the difference between national and California’s
and national SAT scores. Construct a...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 17 minutes ago

asked 25 minutes ago

asked 30 minutes ago

asked 36 minutes ago

asked 47 minutes ago

asked 47 minutes ago

asked 56 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago