Question 10.9: A new machine has been introduced and management is question......
A new machine has been introduced and management is questioning whether it is more productive than the previous one. Management takes 15 samples of this week’s hourly output to test whether it is less productive, and the average production per hour is 1250 items with a standard deviation of 50. The output per hour of the previous machine was 1275 items per hour. Determine with a test of significance whether the new machine is less productive.
The sample mean is 1250, the population mean is 1275, the sample standard deviation is 50 and the sample size is 15.
z={\frac{{\bar{x}}-\mu}{\left[{\frac{s}{\sqrt{n}}}\right]}}={\frac{1250-1275}{\left[{\frac{50}{\sqrt{15}}}\right]}}={\frac{-25}{12.91}}=-0.1936This lies within the range −1.96 to 1.96 and so there is no evidence of any significant difference between the sample mean and the population mean, and so management are unable to make any statement on differences in productivity.