Sample Mean Compared to a Given Population Mean

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Sample Mean Compared to a Given Population Mean The Starting Assumption about the Population

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

Difference of Two Population Means The Starting Assumption about the Populations Ho : u

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