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30 August, 09:25

1) 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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  1. 30 August, 10:54
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    The mean (average) is given as 1200 hours.

    The standard deviation is 200, sample size is 100.

    Find the standard error:

    √ (200^2 / 100) = 20

    Now calculate the confidence interval. For 95% the Z number is 1.96

    Multiply Z by the standard error:

    1.96 x 20 = 39.2

    Now find the range that the mean should be within:

    1200 - 39.2 = 1160.8

    1200 + 39.2 = 1239.2

    The samples should be between 1160.8 and 1239.2 for a 95% confidence interval.

    Since the average was 1050, which is below 1160.8 the bulbs are not in compliance.
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