A manufacturer claims his light bulbs have a mean life $μ = 1800$ hours. A consumer group tested a random sample of $n = 250$ bulbs and found them to have a sample mean life $\bar{x} = 1790$ hours and a sample standard deviation $s = 50$ hours. Assess the manufacturer's claim.
- what is $H_0$?
- What is $H_a$?
- What is the value of the test statistic?
- In what range does the P-value reside?
- Are the results statistically significant at the .05 level of significance?
So I have the following information:
$μ = 1800 = H_O$
$n = 250$
$\bar{x} = 1790 = H_a$
$s = 50$
My test statistic would follow from the equation $\dfrac{\bar x - μ}{s/\sqrt{n}}$, giving $\dfrac{1790 - 1800}{50/\sqrt{250}} = -3.16$. This gives me a P-value of $0.0008$.
This means that the P-value resides in the range $P ≤ 0.01$. I think???
For the last question, I simply don't know what to do. Does it involve finding $Z_{0.05}$, then comparing it with the P-Value?