Simple random sample exercise using α= 5%

Question

One company manufactures steel parts whose diameters follow a normal distribution with μ = 0.5 mm and σ^2 = 0.0784 mm^2. With the aim of increasing homogeneity in production, without modifying the average diameter, the company is adopting a new manufacturing process. After a stabilization period of the new process, an AAS of 31 screws provided a sample mean = 0.53 mm and S^2 = 0.0402 mm^2. Using α = 5%, answer whether the new process is appropriate.

Answer 1

TWO (2) hypothesis tests are needed: (1) for the standard deviation (2) for the mean

 

Chi-square test for comparing the standard deviation:

 

  chi-squareX = (n-1)*s^2 / O^2  = 30* 0.0402^2 / 0.0784^2 = 7.88753384....

 

With 30 degrees of freedom, this test stat is below any of the thresholds listed in the Chi-Square table.

So the standard deviation is within the acceptable range

 

Using the standard deviation with higher variability (the population standard deviation) the normal test stat is

(0.53 - 0.5)/0.0784 = 0.03/0.0784 = 0.382653.....

that is the sample mean lies within 0.382653.. standard deviations from the population mean

 

Once again, this is well below any threshold for the normal distribution.

The statistical evidence supports the hypothesis that the new production scheme is acceptable.