You are raising two breeds of sheep in a shared pasture. After shearing, you collect data on the length of wool (in mm) from 7 Merino sheep and from 7 Cotswold sheep. The data are presented in the table below.

Your null hypothesis is that Merino sheep wool is not significantly different in length than Cotswold sheep wool, and you want to use an alpha of 0.05 throughout your analysis.

Q. What is your conclusion based on your t-statistic and your critical t? What would your decision have been if you instead did a test WITHOUT treating the variances as equal?

Breed WoolLength Merino 65 Merino 65 Merino 68 Merino 70 Merino 71 Merino 72 Merino 74 Cotswold 62 Cotswold 74 Cotswold 76 Cotswold 80 Cotswold 80 Cotswold 81 Cotswold 82a Reject the null hypothesis for both the variances equal test AND for variances unequal test b Fail to reject the null hypothesis for both the variances equal test AND for variances unequal test Fail to reject the null hypothesis for the variances equal test , BUT reject null for the variances unequal C test d Reject the null hypothesis for the variances equal test , BUT fail to reject null for the variances unequal test