Question

Engineers at the American Lighting Company recently developed a new three-way light bulb that they say is more energy efficient than the company’s existing three-way light bulb. The also claim that the bulb will outlast the current bulb, which has an average lifetime of 700 hours. The standard deviation (σ) for the lifetime of bulbs is 75 hours. The American Lighting Company has decided that before it begins full scale production on the new light bulbs it should take a sample of 225 bulbs and determine whether the mean life of the new bulb exceeds the old bulb’s 700 hours. The sample of 225 bulbs gave a sample mean of 704 hours. Assuming a significance level of .05 perform all hypothesis testing steps. Does the sample support the claim that the average lifetime of the new bulb is longer?

Answer 1

Here we need to test the hypothesis for the  American Lighting Company's recently developed three-way light bulb that they say is more energy efficient than the company’s existing three-way light bulb

So, Ho: Xbar new = Xbar old

Ha: Xbar new > Xbar old

At 95% confidence level or 5% significance the z value is 0.8289439 (looking at the z vaue where area under the curve is 95%)

So if the z value is more than 0.8289439 then we will reject the Ho

z= ((Xbar new- Xbar old) - (mu new-mu old))/( σ/sqrt(n))

= (704-700) / (75/sqrt(225)) = 4/5 =0.2

So here the z value is 0.2 which is less than 0.8289439 and hence we conclude that we cannot reject the Ho

And so here we cannot conclude that the  American Lighting Company's recently developed three-way light bulb that they say is more energy efficient than the company’s existing three-way light bulb.

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