Cason read an article claiming that 98.6\%98.6%98, point, 6, percent of births in his country happen in a hospital, 0.5\%0.5%0, point, 5, percent in a home, 0.4\%0.4%0, point, 4, percent in a birthing center, and 0.5\%0.5%0, point, 5, percent in other places. He wondered if the locations of births at his state followed this distribution, so he took a random sample of 200020002000 births and recorded where they happened. Here are his results:
Location Hospital Home Birthing center Other
Births 196819681968 141414 888 101010
He wants to use these results to carry out a \chi^2χ
2
\chi, squared goodness-of-fit test to determine if the distribution of birthing locations in his state disagrees with the claimed percentages.
What are the values of the test statistic and P-value for Cason's test?