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).
Seconds Speed
144 37.5
149.2 36.193029
148.2 36.437247
149 36.241611
149.6 36.096257
146.8 36.784741
148.6 36.339166
149.8 36.048064
149 36.241611
148.2 36.437247
147.8 36.535859
147.2 36.684783
147 36.734694
149.8 36.048064
148.2 36.437247
Calculate independent sample t test for equal variance using the data above?
1 answer