SOLUTION: A factory manufactures light bulbs for distribution under 2 different brands. Brand A bulbs have an average life of 1800 hours with a standard deviation of 240 hours; Those of mar

Question 1205308: A factory manufactures light bulbs for distribution under 2 different brands. Brand A bulbs have an
average life of 1800 hours with a standard deviation of 240 hours; Those of mark B have an average life
of 1450 hours with a standard deviation of 150 hours. A sample of 250 light bulbs is taken from each
brand. Describe completely this situation, define all the data, and explain the method and all steps of
computation. How likely is the average lifespan of Brand A bulbs to be at least 400 hours longer than
that of Brand B bulbs?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this is my best shot at what i think is the way to analyze this.
i'm using a two sample z-test.
referenceto that can be found at

brand A has a mean of 1800 with a standard deviation of 240.
brand B has a mean of 2450 with a standard deviation of 150.
a sample of size 250 is taken from the population of both brands.

the mean of brand A is compared to the mean of brand B using a two sample z-test.
z-score formula is z = (x-m)/s
z is he z-score.
x is the mean of brand A.
m is the mean of brand B.
s is the standard error.

s = sqrt(d1^2/n1 + d2^2/n2)
d1 is the standard deviation of brand A.
d2 is the standard deviation of brand B.
n1 and n2 are the sample size of brand A and brand B.
this is the same at 250.
formula becomes s = sqrt(240^2/250 + 150^2/250) = 17.89972.

z-score formula becomes z = (1800 - 1450) / 17.89972 = 19.55613.
this is a very high z-score, indicating that the mean of brand A is clearly greater than the mean of brand B and that the probability of getting a difference greater than 350 is effectively 0.

based on that, then the probability of getting a mean for brand A that is more than 400 hours greater than the mean for brand B is even less probable, meaning that it is also effectively 0.

here are the results of the two sample t-test using the calculator at https://www.statskingdom.com/120MeanNormal2.html

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