singletary43
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Can someone show me the steps to working this problem out because I got a test on this next week? Thanks for the help in advance.

A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours. A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours. At a 95% confidence level, determine whether these light bulbs are in compliance with the company's claim.

Respuesta :

MissPhiladelphia
You must use the Standard Normal tables for this problem since n (100) is large. 

First find the Confidence Interval (CI), then examine if 1050 falls within the range

CI = mean +/- (z*)(standard deviation)/sqrt n 

where z* comes from the standard normal table with 5%/2 = 0.025 in each tail. 

z* = 1.96 

CI = mean +/- (z*)(standard deviation)/sqrt n 

CI = 1200 +/- (1.96)(200)/sqrt 100 

CI = 1160.8 to 1239.2 

Since 1050 DOES NOT fall within the CI, you would REJECT the hypothesis that these bulbs are in compliance. I hope this helps.

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