What is the Ho and Ha? What is the test statistic (t*)?

Question

Penn State uses thousands of BrightLight fluorescent light bulbs each year. A new manufacturer, AmpleLamp, claims that its new brand of bulbs, which cost the same as the brand the university currently uses, has a mean life of 6000 hours. The university has never studied how long BrightLight bulbs last and they decided they’re curious to see how long BrightLight bulbs last compared to AmpleLamp bulbs. The university decides to conduct a significance test at the =.05 significance level. 64 BrightLight bulbs are tested and the mean life time is found to be 5910 hours. Both manufacturers report that the standard deviation for the lifespan of a light is 400 hours. Are the lifespans of the two brands of lights the same or not?

Answer 1

We are taking one sample, so this is a single mean t-test.

mean = AmpleLamp bulb life

Ho: mean = 6000

Ha: mean != 6000 (two sided test since asking if same or not).

testing Ho using sample data for BrightLight bulb life.

The t-statistic = (sample mean - population mean)/(standard deviation/sqrt(sample size)) where standard deviation = 400, sample mean = 5910 and population mean = 6000 and sample size = 64.