How to check statistical significance?

Question

I have a machine which produces belts with normalized length of 30 cm. Now there is the assumption that the machine works incorrectly and produces belts with a slightly lesser length.

From a test with 100 measurements a mean value of 25 and a standard deviation of 3 cm have been acquired. How could one check these data against a significance level of 0.05? I am somehow stuck..

Answer 1

From Minitab, which accepts summary data, here is output for an appropriate test. The null hypothesis that the population mean remains $\mu = 30,$ is strongly rejected. (Because only summary data are provided, there is no way to check whether data are normal, as required for this one-sample t test.)

One-Sample T 

Test of μ = 30 vs < 30


  N    Mean  StDev  SE Mean  95% Upper Bound       T      P
100  25.000  3.000    0.300           25.498  -16.67  0.000