statistics- mean lifetime of lightbulbs?

Question

A manufacturer claims that the mean lifetime of its bulbs is 1050 hours. A homeowner selects 40 bulbs and finds the mean life time to be 1030 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use α= 0.05

Answer 1

To do this you need
1. Create a 95% confidence interval of the sample
2. See if the population mean falls within that
Note that you are using the t-table not the z table as the variance in unknown...

sample mean +/- t * (sd/sqrt(n))
1030 +/- 2.0227 x (80/(sqrt40))
We are 95% confident that the true mean of the sample distribution falls between these two values
1055.585356
1004.414644

the manufacturers claim on 1050 falls within this region therefor we can conclude that the sample is in line with the claim