Question

CH12 Q6

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 Experience Level Medium Low High Decision (2 years) (2-8 years) 8 years) Pass 152 16 100 27 285 Fail a. Select the competing hypotheses to determine whether the inspector pass/fail decision depends on experience level ๏ Ho: Inspector pass/fail decision and experience level are independent; HA: Inspector pass/fail decision and experience level are dependent. Ho: Inspector pass/fail decision and experience level are dependent; HA: Inspector pass/fail decision and experience level are independent. b. Calculate the value of the test statistic. (Round the intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) est statistic

Answer 1

Answer:

a). First option ( selected option is correct)

b). Test statistic = 8.490

d1).

Reject Ho. At 10% level, we have enough evidence to conclude that inspection pass/fail and experience are dependent.

$\chi^2 = \sum \frac{(O - E)^2}{E}$

Chi-Square Test
Observed Frequencies
	Column variable					Calculations
Row variable	<2 years	2-8 years	>8 years	Total		fo-fe
pass	152	285	100	537		7.4231	1.8702	-9.2933
fail	16	44	27	87		-7.4231	-1.8702	9.2933
Total	168	329	127	624
Expected Frequencies
	Column variable
Row variable	<2 years	2-8 years	>8 years	Total		(fo-fe)^2/fe
pass	144.5769	283.1298	109.2933	537		0.3811	0.0124	0.7902
fail	23.4231	45.8702	17.7067	87		2.3525	0.0763	4.8775
Total	168	329	127	624
Data
Level of Significance	0.1
Number of Rows	2
Number of Columns	3
Degrees of Freedom	2
Results
Critical Value	4.6052
Chi-Square Test Statistic	8.4899
p-Value	0.0143
Reject the null hypothesis