How does hypothesis testing work with the standardized, normalized function in tables?[br][br]In the left-hand graph, we have the normal curve of the actual problem. [br](The curve is centered at the hypothesized mean miH and the standard error is the standard deviation divided by the square root of n.)[br]We calculate the critical value(s) for this curve using InverseNormal(miH,stderr,alpha/tailn) and InverseNormal(miH,stderr,1-alpha/tailn).[br]Then we [b]directly check[/b] our sample mean xbar to see if it is within (do NOT reject Ho) or outside (reject Ho).[br][br]In the right-hand graph, we move to the standardized, normalized PDF (fs) and CDF (p) used in tables.[br]We calculate the critical z value(s) using zc=InverseNormal(0,1,alpha/tailn). Automatically -zc is the other critical value.[br]Then we [b]offset our sample mean xbar [/b]. Here we used the formula directly offset=(difference in means)/stderr. (We could use ZMeanTest.)[br]Finally, we [b]check the offset[/b] to see if it is within (do NOT reject Ho) or outside (reject Ho).

Use the checkbox at right to change between the PDF and CDF (p-value). Make sure you understand all the parts of these graphs.[br]Use the slider to see how changing the sample mean xbar changes the zstat (offset). Does it change more or less than the actual sample mean?[br]Use the slider to see how changing the sample size n affects the graphs. What changes on which graph? Does increasing the sample size mean a greater possibility for rejection or a smaller possibility?[br]Can you write an interesting question to ask your fellow student?[br][br]Here is the R code for standardized, normalized.[br]#Givens[br]#Assume normal distribution[br]miH=3[br]sig=0.9[br]#Assume confidence interval 95%.[br]alpha=0.05[br]#Assume Ho: miH=3 so 2 tails[br]tailn=2[br]#Reject or not reject?[br]n=15[br]xbar=2.78[br][br]stderr=sig/sqrt(n)[br]zc=qnorm(alpha/tailn)[br]offset=(xbar-miH)/stderr[br][br]NotReject= (zc<=offset)&&(offset<=-zc)[br]NotReject[br][br]#miH is the hypothesized mean.[br]#n is the sample size[br]#sig is the standard deviation[br]#stderr=standard error[br]#zc is the standardized, normalized critical z for given significance.