Question

# Previous experience shows the standard deviation of a given process to be 3.7. A manufacturing engineer...

Previous experience shows the standard deviation of a given process to be 3.7. A manufacturing engineer is concerned that the standard deviation has changed. a) State the Hypothesis to show the standard deviation of the process has changed? b) To test the hypothesis, the manufacturing engineer takes a random sample of 12 from the process and records the variable of interest. The data appear in the Process worksheet of the Hypothesis Tests HW data workbook on Moodle. Use JMP to test the hypothesis of part a). c) Using  = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem

Variable

52

44

51

58

48

49

38

49

50

42

55

51

Claim: The standard deviation of the process has changed.

Sample size = n = 12

Sample standard deviation = s = 5.4848

a) The null and alternative hypothesis is  b) Test statistic is  Level of significance = 0.05

Degrees of freedom = n - 1 = 12 - 1 = 11

P-value = P( ) = 0.0120

c) Since P-value is less than the level of significance, We reject the null hypothesis. There sufficient evidence to conclude that the standard deviation of the process has changed.

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