To calculate the independent sample t-test for equal variance using the data above, we need to compare the means of the two groups.
First, we calculate the mean of each group:
Group 1 mean = (37.5 + 36.241611 + 36.096257 + 36.241611 + 36.241611) / 5 = 36.6240208
Group 2 mean = (36.193029 + 36.437247 + 36.784741 + 36.339166 + 36.048064 + 36.437247 + 36.535859 + 36.684783 + 36.734694 + 36.048064 + 36.437247) / 11 = 36.44720636
Next, we need to calculate the variance of each group:
Group 1 variance = ((37.5 - 36.6240208)^2 + (36.241611 - 36.6240208)^2 + (36.096257 - 36.6240208)^2 + (36.241611 - 36.6240208)^2 + (36.241611 - 36.6240208)^2) / 4 = 1.000349864
Group 2 variance = ((36.193029 - 36.44720636)^2 + (36.437247 - 36.44720636)^2 + (36.784741 - 36.44720636)^2 + (36.339166 - 36.44720636)^2 + (36.048064 - 36.44720636)^2 + (36.437247 - 36.44720636)^2 + (36.535859 - 36.44720636)^2 + (36.684783 - 36.44720636)^2 + (36.734694 - 36.44720636)^2 + (36.048064 - 36.44720636)^2 + (36.437247 - 36.44720636)^2) / 10 = 0.056577453
(Note: The variance formula used here is the sample variance formula, dividing by n-1 instead of n.)
With these values, we can now calculate the t-statistic using the formula:
t = (mean1 - mean2) / sqrt((variance1/5) + (variance2/11))
= (36.6240208 - 36.44720636) / sqrt((1.000349864/5) + (0.056577453/11))
= 0.17681444 / sqrt(0.200069973 + 0.00514341)
= 0.17681444 / sqrt(0.205213383)
Finally, we can compare the calculated t-statistic to the critical value to determine if there is a significant difference between the two groups. The critical value depends on the desired level of significance and the degrees of freedom (n1-1 + n2-1 - 2).