There were two independent groups who took a school course by different modes. The first sample of students took the course in the online and the second sample took the course in the conventional face to face mode. Using the sample data determine if there is significant difference in the scores between the two groups .
Ho: (u1-u2=0) no difference
H1: (u1-u2) <> there is a difference
?= 0.05 t critical= +_ 2.01 n
n1= 10, n2=10
m1=93, m2=85
s1=20,s2=20
Statistics and Probability Answers (3)
There were two independent groups who took a school course by different modes. The first sample of students took the course in the online and the second sample took the course in the conventional face to face mode. Using the sample data determine if there is significant difference in the scores between the two groups .
Ho: (u1-u2=0) no difference
H1: (u1-u2) <> there is a difference
?= 0.05 t critical= +_ 2.01 n
n1= 10, n2=10
m1=93, m2=85
s1=20,s2=20
To determine if there is a significant difference in the scores between the two groups, we need to conduct a t-test.
Here's how you can calculate the t-statistic and compare it with the t-critical value:
Step 1: Calculate the pooled standard deviation (sp):
Calculate the variance for each group:
s1^2 = s1^2 / n1 = 20^2 / 10 = 400 / 10 = 40
s2^2 = s2^2 / n2 = 20^2 / 10 = 400 / 10 = 40
Calculate the pooled standard deviation:
sp = sqrt((s1^2 + s2^2) / (n1 + n2 - 2)) = sqrt((40 + 40) / (10 + 10 - 2)) = sqrt(80 / 18) ≈ 3.16
Step 2: Calculate the standard error (SE):
SE = sp * sqrt(1/n1 + 1/n2) = 3.16 * sqrt(1/10 + 1/10) = 3.16 * sqrt(2/10) ≈ 3.16 * 0.632 ≈ 1.99
Step 3: Calculate the t-statistic (t):
t = (m1 - m2) / SE = (93 - 85) / 1.99 ≈ 4.02
Step 4: Compare the calculated t-statistic with the t-critical value:
The critical t-value for a two-tailed test with a significance level of 0.05 and 18 degrees of freedom (n1 + n2 - 2) is approximately 2.01 (as given in the question).
Since the calculated t-statistic (4.02) is greater than the t-critical value (2.01), we reject the null hypothesis (Ho) and conclude that there is a significant difference in the scores between the two groups.
Therefore, based on the sample data, we can say that there is a significant difference in the scores between the online and face to face mode groups.