I have a question regarding the following sampling scenario.
An agricultural cargo (such as rice or coconut) is tested for microbiological contamination such as Salmonella. The cargo consists of 300 bags of the product and a 10g sample is taken from each bag giving 300 x 10g in total. Suppose it was possible to test each 10g sample in turn for Salmonella and zero positive results were obtained. Then a 95% confidence interval for the contamination rate for the cargo would [ 0%, 1% ].
However, the instrument used to detect Salmonella requires a minimum of 100g for the test to be effective. Consequently, the 300 x 10g samples are combined into 30 x 100g samples. This also reduces the time taken to do all tests as only 30 tests have to be done rather than 300.
My question is what is the confidence interval for the contamination rate if zero positives occur. Is it still [ 0%, 1% ] or is it now [ 0%, 10% ] because only 30 tests were done? I feel the confidence interval is still unchanged since even if all samples were combined into a single test, the fact that the test is negative must imply that all of 10g samples were negative. Obviously if there is a positive test then one would have to base the confidence on 30 tests rather than 300 tests.
What do you think?
Thank you in anticipation.
Nigel Marriott
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