# Thread: sample word problem, how to continue?

1. ## sample word problem, how to continue?

μ=82μ=82
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I have this following problem to solve:"A factory produces rods which are planned to have a length of 80 cm. We assume that the length of the rods variates normaly having the normal distribution. We pick a sample of 100 rods and measure the length of each. We have the results that the arithmetic mean of the sample is 82 cm and the variance of the sample is 0,025 cm^2. Test the hypothesis that the length of the rods produced in the factory have the desired value 80 cm. The alternative hypothesis is that the length differs 80 cm from the desired value."

I have solved the value t:

t=μμ0S2n=82800.025100
whe

But how should I continue? What do I have left? This problem is confusing me..
$t = \dfrac{\mu - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}$
$t = \dfrac{82-80}{\sqrt{\frac{0.025}{100}}} \approx 126.5$
At any rate given this statistic the probability that the produced rods conform to a population mean of 80cm (i.e. $H_0$) is 0.