In　this　article,　an　unbalanced　one-way　random　effects　model　is　considered　for　the　log-transformed　shift-long　exposure　measurements.　Exact　test　and　confidence　interval　for　the　proportion　of　workers　whose　mean　exposure　exceeds　the　occupational　exposure　limit　are　developed　based　on　the　concepts　of　generalized　p-value　and　generalized　confidence　interval.　Some　simulation　results　to　compare　the　performance　of　the　proposed　test　with　that　of　the　existing　method　are　reported.　The　simulation　results　indicate　that　the　proposed　method　appears　to　have　significant　gain　in　the　size　and　power.