(Solved): Specifications for the diameter of a roller are \( 2.10-2.11 \mathrm{~cm} \). Rollers that are too ...

Specifications for the diameter of a roller are \( 2.10-2.11 \mathrm{~cm} \). Rollers that are too thick can be reground, while those that are too thin must be scrapped. Three machinists grind these rollers. Samples of rollers were collected from each machinist, and their diameters were measured. The results are as follows: Can you conclude that the proportions of rollers in the three categories differ among the machinists? (a) State the appropriate null hypothesis. (b) Compute the expected values under the null hypothesis. (c) Compute the value of the chi-square statistic. (d) Find the p-value. What do you conclude?