Question 1074706: A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 747 hours. A random sample of 29 light bulbs has a mean life of 737 hours. Assume the population is normally distributed and the population standard deviation is 56 hours. At alphaαequals=0.050, do you have enough evidence to reject the manufacturer's claim? Identify the critical value(s). Use technology.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the claim is that the mean life of the bulb is at least 747 hours.
the sample of size 29 has a standard deviation of 56 and a mean life of 737 hours.
you would think that, if the mean life of the bulb is claiamed to be at least 747 hours, that it would be unusual for the mean life of a sample of 29 bulbs to be less than that.
the critical value for it being unusual is that less than 5% of multiple samples of 29 bulbs should have a mean life less than 747 hours.
what this says is that this particular sample should be unusual since it does have a mean life less than 747 hours.
the critical z-score with an alpha of .05 on the low end is equal to -1.65.
the z-score of the sample is calculated as follows:
z = (x-m)/s
x = 737
m = 747
s = sd / sqrt(n) = 56/sqrt(29) = 10.4
you get z = -10/10.4 = -.96
since the z-score of the sample is less than the critical z-score, than you can conclude that the fact that the mean of this sample is less than the assumed mean of the population is not unusual.
this means that you can expect it to occur in more than 5% of the samples of size 29 taken.
this would cause you to reject the claim that the mean life of this type of bulb is at least 747 hours.
that's my opinion based on the expectation that the mean life of the bulb is at least 747 hours.
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