A sample of 100 electric bulbs produced by manufacturer ‘A’ showed a mean life time of 1190 hrs and an S.D. of 90 hrs A sample of 75 bulbs produced by manufacturer ‘B’ Showed a mean life time of 1230 hrs with S.D. of 120 hrs. Is there difference between the mean life times of the two brands at a significance level of 0.05
Answers
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Concept:
The mean is the average of the supplied numbers and is computed by dividing the total number of numbers by the sum of the given numbers.
Mean = (Summation of all observations/Total observations)
Given:
Number of bulbs manufactured by A = 100
Mean life of bulb manufactured by A = 1190 hours
S.D of bulb manufactured by A = 90 hours
Number of bulbs manufactured by B = 75
Mean life of bulb manufactured by B = 1230 hours
S.D of bulb manufactured by B = 120 hours
Find:
Weather there is significance difference between mean life of both
Solution:
The mean of manufactured A - mean of manufactured B = 1190 - 1230
mean of manufactured A - mean of manufactured B = -40
95 % confidence interval of this difference: From -71.33 to -8.67
t = 2.5204
df = 173
Standard error of difference = 15.871
The two tailed P values equal 0.0126
At 0.01 level, accept null hypothesis.
At 0.05 level, reject null hypothesis.
Hence, At 0.05 level, reject null hypothesis.
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