Question

Use Minitab to create graphs showing the 1-sided critical values for 0.05 and 0.01 in the standard normal.

Distribution Plot Normal, Mean O, StDev 04 02 645 Distribution Plot Normal, Mean 0, StDev-1 04 0.3- 02 0.1 0 0099031 0.0 233

1. Considering one of the graphs you created for part a, give the 2-sided critical value for 0.10 in the standard normal. Briefly explain your answer.
2. Use Minitab to create graphs showing the 1-sided critical values for 0.05 and 0.01 in the t with 63 degrees of freedom. Briefly explain, using what we have discussed about the t distributions, why these values are higher than the corresponding values from part a.

c. Consider the probabilities, 0.005 and 0.01. In the standard normal, will the critical value for 0.01 be greater than or less than the critical value for 0.005? Briefly explain your answer.

d. Consider the probabilities, 0.005 and 0.01. In the t with 63 degrees of freedom, will the critical value for 0.01 be greater than or less than the critical value for 0.005? Briefly explain your answer.

Answer 1

$a.~First~we~consider~Graph~1~showing~1-sided~critical~value~for~0.05.\\ 2~sided~critical~values~for~0.10=\pm1.645~since~2~sided~critical~values\\ ~lies~both~sides~of~the~curve~(left~and~right)~and~total~\\ area=0.05(right)&plus;0.05(left)~so~ its~magnitude~is~same~as~ the~one~sided~critical\\ ~value~for~0.05.\\ b.~Since~t~distribution~is~leptokurtic~whereas~normal~distribution~is~mesokurtic~\\ so~tail~probability~is~higher~for~t-distribution~than~normal~distribution.\\ c.~Since~0.005<0.01~hence~P(Z>Z_{0.005})<P(Z>Z_{0.01})~where\\ Z_{0.005}~and~Z_{0.01}~are~two~critical~values~for~0.005,~0.01~respectively\\ so~the~critical~value~for~0.01~is~less~than~the~critical~value~for~0.005.\\ d.~Using~the~same~argument~as~c,~since~P(t>t_{0.005})<P(t>t_{0.01})~where\\ t_{0.005}~and~t_{0.01}~are~two~critical~values~for~0.005,~0.01~respectively\\ so~the~critical~value~for~0.01~is~less~than~the~critical~value~for~0.005.\\$