Question

coming up with five or six random numbers - for each group if Independent Samples t-test problem) OR coming up with Pre & Post scores for five or six individuals – if it is a Correlated Samples t-test problem. Just coming up with two sets of numbers and labeling them Groups 1 and 2, or Labeling them Pre and Post is all you need to do for this week’s t-test problem.

Answer 1

Suppose we have two independent data sets as,

data1   data2
132   141
145   139
124   172
122   131
165   150
144   125
151  

We have to test,

    Vs

We use Minitab for t-test,

Descriptive Statistics: data1, data2

Variable    Mean StDev Variance
data1     140.43 15.44    238.29
data2     143.00 16.60    275.60

MTB > TwoSample 'data1' 'data2';
SUBC>   Confidence 95.0;
SUBC>   Test 0.0;
SUBC>   Alternative 0;
SUBC>   Pooled.

Two-Sample T-Test and CI: data1, data2

Two-sample T for data1 vs data2

       N   Mean StDev SE Mean
data1 7 140.4   15.4      5.8
data2 6 143.0   16.6      6.8

Difference = μ (data1) - μ (data2)
Estimate for difference: -2.57
95% CI for difference: (-22.13, 16.99)
T-Test of difference = 0 (vs ≠): T-Value = -0.29 P-Value = 0.778 DF = 11
Both use Pooled StDev = 15.9764

_____________________________________________________________________________________

P-value = 0.778 > alpha = 0.05, Do not reject the null hypothesis.
Conclusion -
From given sample information and at level of significance alpha = 0.05, there is not enough evidence to say that the two population averages are different.