MATH 376 -- Probability and Statistics II

Lab Project 3 Solutions

April 14, 2004

A)

>	read "/home/fac/little/public_html/ProbStat/MaplePackage/MSP.map";

Warning, the name changecoords has been redefined

>	XList:=evalf([1250,1210,990,1310,1320,1200,1290,1360,1200,1150,1120,1360,1310,1110,1320,980,950,1430,1100,1080,960,1050,1310,1240,1420,1170,1470,1060,1230,1300]);

>	Xbar:=Mean(XList);

>	S[X]:=StandardDeviation(XList);

>	YList:=evalf([1180,1360,1310,1190,920,1060,1440,1010,1000,950,1310,980,1310,1030,960,800,1280,1080,900,1030,930,1050,1010,1310,940,860,1450,1070,840,1100]);

>	Ybar:=Mean(YList);

>	S[Y]:=StandardDeviation(YList);

1)

>	BoxWhisker(XList,YList);

Here XList (new process) is the bottom, YList (old process) is the top.

The median and 25th %ile are definitely greater for the new process --

guess that   Thus, our null hypothesis is   :   ; alternative hypothesis

is  

>	nops(XList),nops(YList);

so a large sample  Z-test  is appropriate.  

Z =

With   ,  the rejection region is   z >  = 1.645

>	z:=(Xbar-Ybar)/sqrt(S[X]^2/30+S[Y]^2/30);

This is well into the rejection region, so we reject the null hypothesis

at this level.

c)  With ,  the data indicate we have good reason to

reject the null hypothesis in favor of the alternative hypothesis

d)  The attained significance level is:

>	p:=1-NormalCDF(0,1,z);

B)  

1)

>	XListB:=[21.7,21.0,21.2,20.7,20.4,21.9,20.2,21.6,20.6];

>	nops(XListB);

>	XbarB:=Mean(XListB);

>	SB2[X]:=Variance(XListB);

>	YListB:=[21.5,20.5,20.3,21.6,21.7,21.3,23.0,21.3,18.9,20.0,20.4,20.8,20.3];

>	nops(YListB);

>	YbarB:=Mean(YListB);

>	SB2[Y]:=Variance(YListB);

With     being  

>	F:=8*SB2[X]/(12*SB2[Y]);

For a level   two-tail F-test (for instance)

>	1-FCDF(8,12,3.5114);

>	1-FCDF(8,12,.2381);

RR:  F > 3.5114 or F < .2381.

Here   F = .24329 is not in RR, so we do not reject the null hypothesis on the basis of this data.

2)  Since we can work under the assumption that the variances are equal, we use the

t-test for equality of means:

>	S[P]:=sqrt((8*SB2[X]+12*SB2[Y])/20);

>	T:=evalf((XbarB-YbarB)/(S[P]*sqrt(1/9+1/13)));

Rejection region, though, is    >

For instance, for     two-tailed   t-test

>	1-TCDF(20,2.0859);

RR:     >  2.0859

So cannot reject null hypothesis on the basis of this data.

3)

>	BoxWhisker(XListB,YListB);

>	Welch:=(SB2[X]/9+SB2[Y]/13)^2/((SB2[X]/9)^2/8+(SB2[Y]/13)^2/12);

>