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# Lightbulb Factory Means

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The quality-control manager at a lightbulb factory needs to determine whether the mean life of a large shipment of lightbulbs is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 lightbulbs indicates a sample mean life of 350 hours
a. State the null and alternative hypothesis
b. At the 0.05 level of significance is there evidence that the mean life is different from 375 hours?
95% confidence interval
Ho: light bulbs = 375 hours Ho: light bulbs < 375
N=64 xbar=350 M+375 Std dev =64
350-375=-25 std dev divided by the sqr rt of N is 12.5 -25/12.5 is -2 look up on Z table is.0228
Is this correct not sure what to do with other parts of the equation. I know how to get df 64-1=63
At 63 level of significance of .05 is this 1.6694
Unfortunately my professor does not use actual problems from book places formulas only on the board so it is difficult for me to put this all together when reading the entire problem The critical value table he has explained that .05 for instance is 90% and so on so with these questions not sure if you take df or look at the 90%, 95% at the top.
Please explain if possible from the little I apparently am getting.

##### Solution Summary

The quality-control manager at a lightbulb factory needs to determine whether the mean life of a large shipment of lightbulbs is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 lightbulbs indicates a sample mean life of 350 hours
a. State the null and alternative hypothesis
b. At the 0.05 level of significance is there evidence that the mean life is different from 375 hours?
95% confidence interval
Ho: light bulbs = 375 hours Ho: light bulbs < 375
N=64 xbar=350 M+375 Std dev =64
350-375=-25 std dev divided by the sqr rt of N is 12.5 -25/12.5 is -2 look up on Z table is.0228
Is this correct not sure what to do with other parts of the equation. I know how to get df 64-1=63
At 63 level of significance of .05 is this 1.6694
Unfortunately my professor does not use actual problems from book places formulas only on the board so it is difficult for me to put this all together when reading the entire problem The critical value table he has explained that .05 for instance is 90% and so on so with these questions not sure if you take df or look at the 90%, 95% at the top.

##### Solution Preview

Ho: M = 375
<br>H1: M <> 375
<br>*note this is a two-tailed distribution, when we are to test whether the mean life is DIFFERENT FROM 375 ...

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