Question

Do students who take SAT coaching classes improve their test scores? Seven students were selected randomly from all of the students who completed an SAT coaching class in a given year. For each student, the first SAT score (before the class) and the second SAT score (after the coaching class) were recorded. The data is summarized below:

Student 1 2 3 4 5 6 7 First SAT score 920 820 960 920 1060 860 1010 Second SAT score 1030 800 980 980 1140 960 1040

Does this data provide sufficient evidence to conclude that the average SAT score after completing the coaching class was higher than the average score before the class for students in this year’s class?

Your answer should include:

- The parameter for the test and why you chose that parameter.

- The null hypothesis (H0) and alternative hypothesis (Ha ).

- Discussion of the conditions and why they are satisfied or why they are not satisfied. (Regardless of your answer here, assume the conditions are satisfied.)

- The sample statistic and its value.

- The test statistic used and its value

- The P-value and its significance.

- Your conclusion in the context of the claim as stated above

Answer #1

Coaching companies claim that their courses can raise the SAT
scores of high school students. But students who retake the SAT
without paying for coaching also usually raise their
scores. A random sample of students who took the SAT twice found
427 who were coached and 2733 who were uncoached. Starting with
their verbal scores on the first and second tries, we have these
summary statistics:
Try 1 Try 2
Gain
nn
x¯¯¯x¯
ss
x¯¯¯x¯
ss
x¯¯¯x¯...

A certain test preparation course is designed to improve
students' SAT Math scores. The students who took the prep course
have a mean SAT Math score of 507 while the students who did not
take the prep course have a mean SAT Math score of 501. Assume that
the population standard deviation of the SAT Math scores for
students who took the prep course is 45.7 and for students who did
not take the prep course is 32.1 The SAT...

A certain test preparation course is designed to improve
students' SAT Math scores. The students who took the prep course
have a mean SAT Math score of 507 while the students who did not
take the prep course have a mean SAT Math score of 501. Assume that
the population standard deviation of the SAT Math scores for
students who took the prep course is 45.7 and for students who did
not take the prep course is 32.1 The SAT...

Do students tend to improve their SAT math score the second time
they take the test? A random sample of four students who took the
test twice provided the given scores.
Student
1
2
3
4
First Score
450
520
720
600
Second Score
440
600
720
630
Assuming that the change in SAT Math score (second score—first
score) for the population of all students taking the test twice is
Normally distributed with mean μ , are we convinced that...

An SAT prep course claims to improve the test score of students.
The table below shows the scores for seven students the first two
times they took the verbal SAT. Before taking the SAT for the
second time, each student took a course to try to improve his or
her verbal SAT scores. Do these results support the claim that the
SAT prep course improves the students' verbal SAT scores? Let
d=(verbal SAT scores prior to taking the prep course)−(verbal...

For all U.S. students nationally who take the SAT, the average
SAT Math score is 500, with a population standard deviation of 125.
A random sample of 10 students entering Whitmer College had an
average SAT Math (SAT-M) score of 530. The sample data can be used
to test the claim that the mean SAT-M score of all Whitmer College
students is different than the national mean SAT-M score. Based on
the given information, have the conditions for this hypothesis...

An SAT prep course claims to improve the test score of students.
The table below shows the scores for seven students the first two
times they took the verbal SAT. Before taking the SAT for the
second time, each student took a course to try to improve his or
her verbal SAT scores. Do these results support the claim that the
SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep
course)−(verbal...

An SAT prep course claims to improve the test score of students.
The table below shows the scores for seven students the first two
times they took the verbal SAT. Before taking the SAT for the
second time, each student took a course to try to improve his or
her verbal SAT scores. Do these results support the claim that the
SAT prep course improves the students' verbal SAT scores? Let
d=(verbal SAT scores prior to taking the prep course)−(verbal...

9. An SAT prep course claims to improve the test score of
students. The table below shows the scores for seven students the
first two times they took the verbal SAT. Before taking the SAT for
the second time, each student took a course to try to improve his
or her verbal SAT scores. Do these results support the claim that
the SAT prep course improves the students' verbal SAT scores? Let
d=(verbal SAT scores prior to taking the prep...

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