A beverage company bottles soda using an automatic filling machine. When the process is running properly, the mean fill is 12.0 ounces per can. Each day analysts select a random sample of cans and measure the volume of soda in each can. They then test to determine whether the filling process is working properly.

(a) Monday the analysts tested 25 cans and calculated a sample mean of 12.05 ounces and a sample standard deviation of 0.20 ounces. Construct and conduct an appropriate hypothesis test for determining whether the filling machine is working properly. Interpret your result within the context of this problem. Use a 5% level of significance.

(b) Tuesday the analysts tested 225 cans and the calculations revealed that the sample mean is again 12.05 ounces and the sample standard deviation is again 0.20 ounces. Construct and conduct an appropriate hypothesis test for determining whether the filling machine is working properly. Interpret your result within the context of this problem. Use a 5% level of significance.

(c) Explain any differences in your conclusions in parts (a) and (b). Be specific and use statistical reasoning.