The length of life (in hours) of a sample of 40 100-watt light bulbs manufacture

Question

The length of life (in hours) of a sample of 40 100-watt light bulbs manufactured in aSylvania plant and a sample of 40 100-watt light bulbs manufactured in a Phillips plant arecontained in tab Bulb Life in the Excel file.   In order to analyze the difference in bulb life fromthese two manufacturers, determine whether the variances are equal and then run theappropriate t-test to test the hypothesis that the mean bulb life of Sylvania bulbs is differentthan 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

Explanation / Answer

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

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