The quality manager believes there may be a relationship between the experience
ID: 3174626 • Letter: T
Question
The quality manager believes there may be a relationship between the experience level of an inspector and whether a product passes or fails inspection. Inspection records were reviewed for 630 units of a particular product, and the number of units which passed and failed inspection was determined based on three inspector experience levels. The results are shown in the following table. a. Specify the competing hypotheses to determine whether the inspector pass/fail decision depends on experience level. H_0: Inspector pass/fail decision and experience level are independent; HInspector pass/fail decision and experience level are dependent. H_0: Inspector pass/fail decision and experience level are dependent; H_A: inspector pass/fail decision and experience level are independent. b. Calculate the value of the test statistic. c. Approximate the p-value. p-valueExplanation / Answer
H0: Inspector pass/fail decision and experience level are independent
HA: Inspector pass/fail decision and experience level are dependent
Test statistic 2= 6.877
So, 0.025<=p-value<0.05
D2. Do not reject H0. At the 1% significance level we have not enough evidence to conclude that the inspection pass/fail and experience are dependent.
Chi-Square Test
Observed Frequencies
Experience Level
Decision
Low
Medium
High
Total
Pass
152
287
103
542
Fail
16
46
26
88
Total
168
333
129
630
Expected Frequencies
Experience Level
Decision
Low
Medium
High
Total
Pass
144.5333
286.4857
110.981
542
Fail
23.46667
46.51429
18.01905
88
Total
168
333
129
630
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991465
Chi-Square Test Statistic
6.876935
p-Value
0.032114
Reject the null hypothesis
Expected frequency assumption
is met.
Chi-Square Test
Observed Frequencies
Experience Level
Decision
Low
Medium
High
Total
Pass
152
287
103
542
Fail
16
46
26
88
Total
168
333
129
630
Expected Frequencies
Experience Level
Decision
Low
Medium
High
Total
Pass
144.5333
286.4857
110.981
542
Fail
23.46667
46.51429
18.01905
88
Total
168
333
129
630
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991465
Chi-Square Test Statistic
6.876935
p-Value
0.032114
Reject the null hypothesis
Expected frequency assumption
is met.
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