The New York Times,May 25, 2006, pp C1, C6) reported that for one insurance company, 85.1% of the claims ...

     6) Late payment of   medical claims can add to the 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 one insurance company, 85.1% of the   claims were paid in full when first submitted. Suppose that the insurance   company developed a new payment system in an effort to increase this   percentage. A sample of 200 claims processed under this system revealed that   180 of the 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) Compute the p-value and interpret its   meaning.