Question

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 SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.05α=0.05 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Student Score on first SAT Score on
second SAT

1 540 560

2 570 610

3 460 500

4 410 510

5 530 550

6 590 620

7 480 530

Step 1 of 5:

State the null and alternative hypotheses for the test.

Step 2 of 5:

Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5:

Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5:

Make the decision for the hypothesis test.

Answer #1

Step 1

To Test :-

H0 :- µd = 0

H1 :- µd < 0

Step 2

S(d) = √(Σ (di - d̅)2 / n-1)

S(d) = √(4542.8571 / 7-1) = 27.5

Step 3

d̅ = Σ di/n = -300 / 7 = -42.8571

t = d̅ / ( S(d) / √(n) )

t = -42.8571 / ( 27.5162 / √(7) )

t = -4.121

Step 4

Reject null hypothesis if t < - t(α)

Critical value t(α) = t(0.05) = 1.9432

t < -1.9432

Step 5

t < - t(α) = -4.1208 < -1.9432

**Result :- Reject null hypothesis**

There is sufficient evidence to support the claim that SAT prep course improves the student's verbal SAT scores.

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...

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...

Student
1
2
3
4
5
6
7
Score on first SAT
530
410
380
600
480
440
380
Score on second SAT
560
460
400
620
500
520
430
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...

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...

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