Sample Mean Compared to a Given Population Mean The Starting Assumption about the Population Ho : u = uo (a given value) Ho is actually TRUE Ho is actually FALSE Correct Conclusion : 1) "I do not reject the null hypothesis because...p-value ≥ alpha" 2) "There is NOT sufficient statistical evidence to reject Ho. I conclude that there the true population means is uo (the given value)” OR 2) “There is NOT sufficient statistical evidence to reject Ho therefore the true population mean is NOT different than uo.” [watch out for double-negatives!] Type II Error Type I 1) "I reject the null hypothesis because....p-value < alpha" 2) “There is sufficient statistical evidence that the true population mean is different than uo (the given value). [or less than… or greater than...]" 2) "There is sufficient statistical evidence that the true population mean is NOT equal to uo [or less than… or greater than...]" Do NOT Reject Ho Our Conclusion from the Sample Data Reject Ho

Difference of Two Population Means The Starting Assumption about the Populations Ho : u1 = u2 Ho is actually TRUE Ho is actually FALSE Correct Conclusion : 1) "I do not reject the null hypothesis because...p-value ≥ alpha" 2) "There is NOT sufficient statistical evidence to reject Ho therefore the the true population means are statistically the same.” OR 2) "There is NOT sufficient statistical evidence to reject Ho. I conclude that there is NO difference between the true population means.” [watch out for double-negatives!] Type II Error Type I 1) "I reject the null hypothesis because....p-value < alpha" 2) "There is sufficient statistical evidence to conclude that there is a difference in the population means.” [or less than… or greater than...] 2) "There is sufficient statistical evidence to conclude that the population means are NOT the same.” Do NOT Reject Ho Our Conclusion from the Sample Data Reject Ho