Question

1. You are a teacher and want to analyze if your morning class has significantly different scores than your afternoon class. You have 12 students in both of your classes. Compute a t-test for independent samples on these scores from the last quiz you administered and then use the eight steps to test the null hypothesis that there is no difference between the two conditions. Do the two groups differ?
Morning class Afternoon class
87 86
98 73
75 79
88 56
76 72
85 70
92 87
56 59
89 64
85 77
84 74
92 72

Answer 1

Let X: Data from morning class and Y: Data from afternoon class

Step I: Set up the Null and Alternative hypotheses:

H0: There is no difference between these two conditions; that is

  

H1: There is difference between these two conditions; that is

Step II: Computing sample means ( and ) and sample standard deviations (s1 and s2) for X and Y

Step III: Computing t test statistic under the null hypothesis is:

Step IV: Computing t critical value for assuming significance level (alpha) 0.05 (alpha is not given hence assumed):

First we have to compute degrees of freedom (df) for independent samples using below formula,

therefore, critical t value for two tailed test, alpha=0.05 and df=22 is -/+2.074

Step V: Computing p-value:

p = p(t2.7575) = 2*p(t < 2.7575) = 2*0.0057 = 0.0115

Step VI: Decision based on p-value:

Since, p value = 0.0115 is less than significance level = 0.05, we reject the null hypothesis

Step VII: Decision based on t value:

Since calculated t = 2.7575 is greater than critical t = 2.074, we reject the null hypothesis

Step VIII: Conclusion:

From the above decisions, we conclude that there is sufficient evidence to claim that there is difference between two population means (i.e.: )