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.

Question

10-01-2017
Mathematics

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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.

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MissPhiladelphia MissPhiladelphia · Answer 1 · 2017-01-12T16:05:06+01:00

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.