Misued? Percent Information

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… Is this statement correct?
      To examine this statement let us make a preliminary assumption about the prevalence of this type of cancer. Let us suppose that the previous detection process yields positive results for 4% of the population tested; the new process would detect 25% more than this. A 25% increase would raise this 4% of the population testing positive to 5% testing positive. How many people would have negative tests with each process? (Recall that a negative test is one in which no cancer is detected.)
      The original detection process identified 96% as having negative results. The new improved process identified 95% as having negative results. If this were applied to a typical group of 100 people, one person of the original 96 found to be negative by the original process is now identified by the new process as apparently having this specific cancer. This one person represents 1.04% of the 96, not 25% as the announcer thought.
      We performed this computation with the assumption that 4% tested positive using the original process. …
…
      The radio announcer would have been correct if 50% of the population tested positive for this cancer using the original process. This is extremely unlikely. The actual incidence of cancer is probably nearer the small values of x …

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source: MISUSING MEDICAL PERCENTS
David R. Duncan and Bonnie H. Litwiller
University of Northern Iowa
Cedar Falls, IA 50614