To defend a governmental institution against corruption, its chief officer claims that less than 0.5% of the its 5000 employees accept bribes. An independent human rights team interviewed 200 people from the company and found only 3 people to have accepted bribes.  Test the claim of the institution chief officer. Use significance level of 5% and then 1%. Find the P-Value for the test.

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To defend a governmental institution against corruption, its chief officer claims that less than 0.5% of the its 5000 employees accept bribes. An independent human rights team interviewed 200 people from the company and found only 3 people to have accepted bribes. 

  1. Test the claim of the institution chief officer. Use significance level of 5% and then 1%.
  2. Find the P-Value for the test.
  3. Assuming that the true mean for the corrupted employees is 10% larger than that obtained by the independent team, and using their own results, determine the number of the employees to be interviewed to detect the true mean, use an allowed error in the test of 5%.
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