A random sample of 100 electric light bulbs produced by manufacturer A showed a mean lifetime of 1990 hours and a standard deviation of 90 hours. A random sample of 75 bulbs produced by manufacturer B showed a mean lifetime of 1230 hours and a standard deviation of 120 hours. Is there a significant difference in the mean lifetimes of the bulbs produced by the two manufacturers at the 0.01 level of significance?
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Let X be lifetime of electric light bulbs
nA = 100
XAmean = 1990
S^2XA = 8100
nB = 75
XBmean = 1230
S^2XB = 14400
H0: μxA = μxB
H1: μxA ≠ μxB, α = 0.01
S(xA - XB) = sqrt(S^2xA/nA - S^2xB/nB) = sqrt(8100/100 + 14400/75) = 16.52271164
Decision Rule:
If abs(((1990 - 1230) - 0)/16.52271164) > z(0.995), Reject H0.
If 46 > 2.575, we Reject H0.
Conclusion:
There is a significant difference in the mean lifetimes of the bulbs produced by the two manufacturers at the 0.01 level of significance.
nA = 100
XAmean = 1990
S^2XA = 8100
nB = 75
XBmean = 1230
S^2XB = 14400
H0: μxA = μxB
H1: μxA ≠ μxB, α = 0.01
S(xA - XB) = sqrt(S^2xA/nA - S^2xB/nB) = sqrt(8100/100 + 14400/75) = 16.52271164
Decision Rule:
If abs(((1990 - 1230) - 0)/16.52271164) > z(0.995), Reject H0.
If 46 > 2.575, we Reject H0.
Conclusion:
There is a significant difference in the mean lifetimes of the bulbs produced by the two manufacturers at the 0.01 level of significance.