SOLUTION: Suppose you were the manufacturer of a new and improved light bulb that you claim has an average service life more than twice the life of your nearest competitor�s product. You

Question 436815: Suppose you were the manufacturer of a new and improved light bulb that you claim has an average service life more than twice the life of your nearest competitor�s product. You want to test your product to be sure. You test 500 of your bulbs in the lab and find that the average life of your bulbs is 2021 hours. Your competitor claims an average service life of 1000 hours. What hypotheses would you test? State the null and alternative hypotheses both verbally and algebraically.
Note: Please do not try to actually complete this hypothesis test. You can't do it, because I don't have the necessary data. Even if I had the necessary data, the scenario was carefully chosen for which I do not know the mathematical equation for the test statistic. For that matter, I'm not sure I know it -- there may not be one. This specific scenario serves as an exercise in correctly forming hypotheses. If you can correctly form these hypotheses, you can probably set up any hypothesis test correctly.

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

where = average lifetime of new lightbulb, and
= average lifetime of old lightbulb.
Commentary: Lightbulb lifetime is usually normally distributed, and thus the random variable is normally distributed with mean . I'm mentioning this information because all we really need are estimates of the standard deviations of the two samples to carry out a test of significance (plus the sample size for your competitor's lghtbulbs.) In this case a large sample z-test is recommendable, and the hypotheses can be rephrased as

.

RELATED QUESTIONS
A light bulb company claims that the 40 watt light bulb it sells has an average life of... (answered by Theo)

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb... (answered by Theo)

Perform a hypothesis test for the following problem. Use the same format as the... (answered by stanbon)

A light bulb manufacturer claims his light bulbs will last 500 hours on the average. The... (answered by stanbon)

Specify the null hypothesis and alternative hypothesis i each of the following cases,... (answered by stanbon)

Specify the null hypothesis and alternative hypothesis in each of the following cases, (answered by stanbon)

Specify the null hypothesis and alternative hypothesis in each of the following cases, (answered by ikleyn)

Q) Specify the null hypothesis and alternative hypothesis in each of the following... (answered by stanbon)

A new type of light bulb has an average lifespan of 1200 hours with a standard deviation... (answered by ewatrrr)