The length of life (in hours) of a sample of 40 100-watt light bulbs manufacture
ID: 3393694 • Letter: T
Question
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 Sylvania Phillips 684 819 926 1020 831 907 946 1077 859 952 984 1113 893 994 1052 1174 922 1016 773 897 939 1038 852 942 972 1096 870 986 1016 1153 909 1007 697 836 926 1022 835 912 954 1077 860 959 1005 1113 899 1004 1080 1188 924 1018 821 903 943 1072 852 943 977 1100 876 992 1041 1154 911 1015 720 888 938 1034 848 918 971 1082 868 962 1014 1116 905 1005 1093 1230Explanation / 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
[ANSWER]
We have evidence to indicate that the mean bulb life of Sylvania bulbs is different than the mean bulb life of Phillips bulbs
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