You are a school psychologist interested in whether a new educational program, Go4It, improves SAT scores in senior high school students. After implementing the educational program in an SAT course at Park High School, you obtain the students’ SAT scores (n = 10). You want to know whether SAT scores from your sample of students, who were enrolled in the Go4It program, are different from the population of SAT scores. You have access to SAT scores for all senior high school students in 2017 (μ = 500) and want to compare that with your obtained sample. Use the 6 steps of hypothesis testing to determine whether SAT scores from students who received the Go4It program (i.e., your sample of 10 students) differ from SAT scores in 2017. The data is provided below. Conduct the appropriate statistical test either by hand or via SPSS, record your answers on the answer sheet, and attach SPSS output.
ID |
SAT Score |
1 |
643 |
2 |
646 |
3 |
553 |
4 |
696 |
5 |
503 |
6 |
534 |
7 |
604 |
8 |
604 |
9 |
593 |
10 |
625 |
a) What is the mean of the population (0.5 pt) and the mean of the sample (0.5)? (1 pt)
b) What is the appropriate statistical test to answer question? (0.5 pt)
c) Step 1: What is your prediction regarding the results of the statistical test? (0.5 pt)
d) Step 2: Set up hypotheses (2 pts)
H_{0} (1 pt):
H_{1} (1 pt):
e) Step 3: Set criteria for decision (2 pts)
Critical value (1 pt):
Decision Rule (1 pt):
f) Step 5: Report Results (2 pts) – Must include test statistic (0.5 pt), degrees of freedom (0.5 pts), p-value (0.5 pt), and appropriate measure of effect size (0.5 pt)
g) Step 6: Interpret the results of the statistical test
in terms of the research question (1 pt)
SPSS DATA
(First Section = Sub ID)
(Second Section = SAT Score)
1 643
2 646
3 553
4 696
5 503
6 534
7 604
8 604
9 593
10 625
a) = 500
= (643 + 646 + 553 + 696 + 503 + 534 + 604 + 604 + 593 + 625)/10 = 600.1
s = sqrt(((643 - 600.1)^2 + (646 - 600.1)^2 + (553 - 600.1)^2 + (696 - 600.1)^2 + (503 - 600.1)^2 + (534 - 600.1)^2 + (604 - 600.1)^2 + (604 - 600.1)^2 + (593 - 600.1)^2 + (625 - 600.1)^2)/9) = 57.6
b) We will use t-test statistic.
d) H_{0}: = 500
H_{1}: 500
e) At 5% significance level, the critical values are t_{0.025, 9} = +/- 2.262
Reject H_{0}. if t < -2.262 or t > 2.262
f) The test statistic t = ()/(s/)
= (600.1 - 500)/(57.6/)
= 5.5
df = 10 - 1 = 9
P-value = 2 * P(T > 5.5)
= 2 * (1 - P(T < 5.5))
= 2 * (1 - 0.9998)
= 0.0004
Effect size = ()/s
= (600.1 - 500)/57.6
= 1.7378
g) Since the test statistic value is greater than the upper critical value(5.5 > 2.262), so we should reject the null hypothesis.
So at 5% significance level, we can conclude that the SAT scores from students who received the Go4lt program differ from SAT scores in 2017.
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