Late payment of medical claims can add to cost of health care. An article (M. Freudenheim, "The Check Is Not in the Mail," The New York Times, May 25, 2006, pp. C1, C6) reported that for 1 insurance company, 85.1% of the claims were paid in full when first submitted. Assume that the insurance company developed the new payment system in an effort to raise this percentage. A sample of 200 claims processed under this system revealed that 180 of claims were paid in full when first submitted.
a. At the 0.05 level of significance, is there evidence that the population proportion of claims processed under this new system is higher than the article reported for the previous system?
b. Calculate the p-value and interpret its meaning.