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.

Decision	Experience Level
	Low (< 2 years)			Medium (2-8 years)			High (> 8 years)
Pass		150			285			101
Fail		18			46			27

a. Select the competing hypotheses to determine whether the inspector pass/fail decision depends on experience level.

• H₀: Inspector pass/fail decision and experience level are independent; H_A: Inspector pass/fail decision and experience level are dependent.

• H₀: 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. (Round the intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c. Find the p-value.

• 0.01 p-value < 0.025

• p-value < 0.01

• 0.025 p-value < 0.05
• p-value 0.10
• 0.05 p-value < 0.10

d-1. At the 1% significance level, what is your conclusion?

d-2. Does your conclusion change at the 10% significance level?

• Yes

• No

Answer 1

The statistical software output for this problem is :

Contingency table results: Rows: Ď Columns: None 22-8 >8 Total Pass 150 285 101 536 Fail 18 4627 91 Total 168 331 128 627 Chi-Square test: Statistic DF Value P-value Chi-square 2 6.5228387 0.0383

H₀: Inspector pass/fail decision and experience level are independent; H_A: Inspector pass/fail decision and experience level are dependent.

Test statistics = 6.523

0.025 p-value < 0.05

d-1 : Fail to reject the null hypothesis

d-2 : es