(Use Excel) The quality manager believes there may be a relationship between the

Question

(Use Excel) 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 622 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 (under 2 years) Medium (2-8 years) High (over 8 years) Pass 153 287 101 Fail 15 44 22 a. Specify 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; HA: Inspector pass/fail decision and experience level are dependent. H0: 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.) Test statistic c. Approximate the p-value. p-value Picture 0.10 p-value < 0.01 0.05 Picture p-value < 0.10 0.01 Picture p-value < 0.025 0.025 Picture p-value < 0.05 d-1. At the 1% significance level, what is your conclusion? H0. At the 1% significance level, we conclude that inspection pass/fail and experience are dependent. d-2. Does your conclusion change at the 10% significance level? Yes No

Explanation / Answer

The statistical software output for this problem is:

Contingency table results:
Rows: var4
Columns: None

Chi-Square test:

Hence,

a) Hypotheses:

H0: Inspector pass/fail decision and experiencelevel are independent.

HA: Inspector pass/fail decision and experience level are dependent.

b) Test statistic = 5.076

c) 0.05 < p-value < 0.10

d - 1) Do not Reject Ho

d - 2) Yes

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