3- An hypothesis test is performed with H0: µ=600 and Ha: µ 600 using a 95% conf

Question

3- An hypothesis test is performed with H0: µ=600 and Ha: µ 600 using a 95% confidence. The x1 and x2 values that define the upper and lower bounds of the test are identified in the figure. The actual process has shifted to a mean of 610. The sample size is 40 and s=20. What is the power of the hypothesis test to detect the shift?

4- In establishing a control chart, the reason for considering initially developed control limits as "trial" limits is?

5- The value D3 used in establishing control charts is used to?

6- An chart with n=5 has been established for a process with = 34.1 and = 4.8. During production, a sample was taken and the pieces measured 33, 31, 38, 42, and 35. For this sample?

7- A controlled process has a mean of 50.1 and variance of 0.04. The specification limits for a part on the process are 50±0.5. Cpk for this process is?

8- A process which is in statistical control?

Explanation / Answer

Q 3.95% confidance interval on nul hypothesis.

= 600 +- Z0.05 (s/n) = 600 +- 1.96 * (20/ 40) = 600 + 6.198 = 606.20

so Power = Pr( Xbar > 606.20; 610; 3.1622)

Z = (606.20 - 610)/ 3.1622 = -1.20

so Pr( Xbar > 606.20; 610; 3.1622) = 1 - (-1.2) = 1- 0.1151 = 0.8849

so the power of this hypothesis test to detect the shift is 88.49%

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