Late payment of medical claims can add to the cost of

Question

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.