My friends and I are in desperate need of statistics help fo

My friends and I are in desperate need of statistics help for our E-280 class... The following data pertains to the question in need of answering:

The length of life (in hours) of a sample of 40 100-watt light bulbs manufactured in a Sylvania plant and a sample of 40 100-watt light bulbs manufactured in a Phillips plant are contained in tab Bulb Life in the Excel file. In order to analyze the difference in bulb life from these two manufacturers, determine whether the variances are equal and then run the appropriate t-test to test the hypothesis that the mean bulb life of Sylvania bulbs is different than the mean bulb life of Phillips bulbs at the .05 level of significance. State your conclusion and the basis for your conclusion.

Sylvania Phillips
684 819
831 907
859 952
893 994
922 1016
939 1038
972 1096
1016 1153
697 836
835 912
860 959
899 1004
924 1018
943 1072
977 1100
1041 1154
720 888
848 918
868 962
905 1005
926 1020
946 1077
984 1113
1052 1174
773 897
852 942
870 986
909 1007
926 1022
954 1077
1005 1113
1080 1188
821 903
852 943
876 992
911 1015
938 1034
971 1082
1014 1116
1093 1230

Solution

Set Up Hypothesis
Null,Ho: u1 = u2
Alternative,mean bulb life of Sylvania bulbs is differentthan the mean bulb
life of Phillips - H1: u1 != u2
Test Statistic
X(Mean)=909.65
Standard Deviation(s.d1)=94.3052 ; Number(n1)=40
Y(Mean)=1018.35
Standard Deviation(s.d2)=96.9014; Number(n2)=40
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (39*8893.471 + 39*9389.881) / (80- 2 )
S^2 = 9141.676
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
to=909.65-1018.35/Sqrt((9141.676( 1 /40+ 1/40 ))
to=-108.7/21.38
to=-5.084
| to | =5.084
Critical Value
The Value of |t | with (n1+n2-2) i.e 78 d.f is 1.991
We got |to| = 5.084 & | t | = 1.991
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -5.0843 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho

[ANSWER]

We have evidence to indicate that the mean bulb life of Sylvania bulbs is different than the mean bulb life of Phillips bulbs