Question
In: Math
To evaluate the performance of inspectors in a new company, a quality manager had a sample...
To evaluate the performance of inspectors in a new company, a quality manager had a sample of 12 novice inspectors evaluate 200 finished products. The same 200 items were evaluated by 12 experienced inspectors. SD of error for the novice inspectors was 8.64 and for the experiences inspectors was 5.74.
Was the variance in inspection errors lower for experienced inspectors than for novice inspectors? Conduct a hypothesis testing at alpha = 0.05 and show all the work.
Solutions
Expert Solution
The provided sample variance is s^2 = 5.74 and the sample size is given by n = 12.
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: 
≤ 8.64
Ha: >
8.64
This corresponds to a right-tailed test, for which a Chi-Square test for one population variance will be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05.
(3) Test Statistics
The Chi-Squared statistic is computed as follows:
(4) Decision about the null hypothesis
Since it is observed that 
, it is then concluded that the null hypothesis is not
rejected.
(5) Conclusion
It is concluded that the null hypothesis Ho is not
rejected. Therefore, there is not enough evidence to claim
that the population variance is greater
than 8.64, at the 0.05 significance level.
the variance in inspection errors lower for experienced inspectors than for novice inspectors? Yes
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