(1)(a) The director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer's specifications which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces of the cloth reveals a sample mean breaking strength of 69.1 pounds. Can it be concluded that there is sufficient evidence that the machine is not meeting the manufacturer's specification for average breaking strength at the 5% level of significance?

(b)If a sample of 25 pieces of this cloth was taken and the mean breaking strength and standard deviation are found to be 69.1 pounds and 3.5 pounds respectively, would this sample produce any evidence about the

machine that is different from what was observed in part (a) of this question? (use the same 5% level of significance in your analysis)