1. 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

2. 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