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3. (30 points) Light-Bulbs-R-us (LIBRUS) says that the average life of their Bright light bulb is at least 1000 hours with standard deviation 240 hours. The Consumer Truth Organization (CTO) selects 36 bulbs and finds their average lifespan is 950 hours. Can CTO question LIBRUS’s claim? (Use a 5% level of significance.) [Make sure to state the null and alternative hypothesis clearly.]
St dev : 240 , a= 0.05
Ho m= At least 1000 (claim)
H1m = less than 1000
950-1000/ 240sq rt 36= -50/40= -1.25
Critical z score is 0.0500 = -1.65
Z score = -1.25
This is a left tailed test. Z score -1.25 falls with in do not reject with a 0.05 level of significance.
St dev = 240 , alpha = 0.05
H_0 mu>=1000 (claim)
H1 mu less than 1000
sigma_xbar=240/sqrt(36)=40
(950-1000)/ 40= -50/40= -1.25
Reading the chart (in the forwards direction) we see that
P=10.6%, which is > alpha.
Hence, we do not reject H_0.
Again someone please write a sentence with the conclusion for participation points.
I am not sure what is the “critical z score” from Aziza R. or where -1.65 comes from.
Also i have a doubt about the graph. The mean from the sample x is 950, but the z is -1.25. How could that be if the z of -1 is 760? Can anyone help me understand?
My response to Aziza was treated in some weird way (I guess any thing between a less than and a greater than is treated as an internal comment and is not printed), so I have redone it by replacing the symbol < with the word less than and now it comes out. To answer Leonardo's question, you must first find the standard deviation of the sample mean which is 240/sqrt(36)=40 so a zscore of -1 is 960 and not 760. Leonardo did attach a picture of his work which included his diagram, but he has used the wrong standard deviation so someone should submit a correct picture.
Here is my picture
This is my conclusion and the picture
Conclusion:
Tests done on the light bulbs of this company a 5% level of significance, resulted minor deviation from the claim of the manufacturer that their bulbs last at least 1000 hours and was found to to be unnecessary to reject the null hypothesis.
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