Question

Compute both a paired t-test and two-sample t-test (for practice) but report the t-value for the correct test.

XI (Girl Guides)	X2 (Boy Scouts)
9	6
9	7
5	5
10	8
6	5
8	6
6	7
7	5
9	4
6	7

Answer 1

Two Sample T-test

The following null and alternative hypotheses need to be tested:

Ho: μ1​ = μ2​

Ha: μ1​ ≠ μ2​

Hence, it is found that the critical value for this two-tailed test is t_c = 2.101, for alpha = 0.05 and df = 18

Since it is assumed that the population variances are not equal, the t-statistic is computed as follows:

So, the observed value is greater than the critical value, it is then concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

Paired t-test

H0: UD = U1 - U2 = 0, where UD equals the mean of the population of difference scores across the two measurements.

The t statistic is given by

Difference Scores Calculations

Mean: -1.5
μ = 0
S2 = SS⁄df = 30.5/(10-1) = 3.39
S2M = S2/N = 3.39/10 = 0.34
SM = √S2M = √0.34 = 0.58

T-value Calculation

t = (M - μ)/SM = (-1.5 - 0)/0.58 = -2.58

p-value = 0.0289, p-value< alphs(=0.05), so we reject the null hypothesis.

The correct for this data is two-sample t-test with unequal variance, as there is independency between the two variables.

And the statistic for this test is = 2.237