Steel rod diameters

Topic: Testing examples · more questions on this topic
‹ A later poll on leaving A shuffling machine ›

Rods should be at least 6 cm in diameter. A sample of 100 rods has mean 6.1 cm and standard deviation 0.1 cm. Assume a normal model.

  1. Estimate the probability that a single rod is thinner than 6 cm.

  2. If the standard deviation stays 0.1 cm, what mean diameter makes 99% of rods at least 6 cm? Use z_{0.99}=2.326.

  3. Test H_0:\mu=6 against H_1:\mu>6. The observed t statistic on 99 degrees of freedom is enormous. What is the conclusion?

  1. (6-6.1)/0.1=-1, and \Phi(-1)=0.1587, about 0.159.

  2. The 0.01 quantile of a normal law sits 2.326 standard deviations below the mean, so the mean must be 6+2.326\times 0.1=6.23 cm.

  3. t=(6.1-6)/(0.1/\sqrt{100})=10 on 99 degrees of freedom. The one-sided p-value is negligible, so the mean diameter is greater than 6 cm.