Answer to Question #329740 in Statistics and Probability for lulu io

Question

Ten cartoons are taken at random from an automatic filling machine. The mean net weight of the 10 cartoons is 11.8 kg and standard deviation is 0.15 kg. Does the sample mean differ significantly from the intend weight of 12 kg. Use 5% level of significance.

Answer 1

Let $\mu=11.8~kg,~\sigma=0.15~kg,~\mu_0=12~kg$

t-value for 10 - 1 = 9 degrees of freedom and 0.05 level of significance is 1.833.

With given level of significance real mean is less than $\mu+t\frac{\sigma}{\sqrt{n}}=11.8+1.833\frac{0.15}{\sqrt{10}}\approx11.887~(kg)$

The value of 12 is greater than 11.887, so the difference is significant.