Larry’s Light Bulb Emporium claims that, on average, their light bulbs

| August 30, 2017

Question
Larry’s Light Bulb Emporium claims that, on average, their light bulbs last more than 500 hourslonger than light bulbs produced by their competitor Billy’s Bright Bulbs. Two independentsamples of fifteen 100W light bulbs from each company are used in the same model of lamp andthe lifetime of each light bulb is measured. The average life of Larry’s light bulbs is found to be10,400 hours, with a standard deviation of 1,200 hours. Billy’s light bulbs lasted a mean of 9,600hours, with a standard deviation of 900 hours. You may assume that the time until failure of thelight bulbs follows a normal distribution. Conduct an appropriate hypothesis test to test Larry’sclaim at the 5% level of significance. Conduct this test using (i) the p-value method and (ii) the critical value method.

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