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). Use a significance level of α=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 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Score on first SAT | 500 | 370 | 430 | 420 | 530 | 450 | 470 |
Score on second SAT | 540 | 410 | 4490 | 460 | 560 | 490 | 490 |
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.
Solution:
Here, we have to use paired t test.
H0: µd = 0 versus Ha: µd < 0
This is a lower tailed test.
Step 2
Sd = 1521.3
Step 3
Test statistic for paired t test is given as below:
t = (Dbar - µd)/[Sd/sqrt(n)]
From given data, we have
Dbar = -610
Sd = 1521.3262
n = 7
df = n – 1 = 6
t = (-610 – 0)/[ 1521.3262/sqrt(7)]
t = -1.0609
P-value = 0.1648
(by using t-table)
Step 4
We reject H0 when P-value < 0.05
Step 5
P-value > α = 0.05
So, we do not reject the null hypothesis
There is not sufficient evidence to conclude that an SAT prep course improve the test score of students.
An SAT prep course claims to improve the test score of students. The table below shows...
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...
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...
Question 7 - of 17 Step 2 of 5 01:38:52 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). Use a significance level of α=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 1 2 3 4 5 6 7 Score on first SAT 540 410 430 470 580 450 410 Score on second SAT 570 440 460 500 600 520 460 Step...
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