A hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain period. Nationally the readmission rate for patients with pneumonia is 17%. A hospital was interested in knowing whether their readmission rate for pneumonia was less than the national percentage. They found 11 patients out of 70 treated for pneumonia in a two-month period were readmitted.

a. What is pn, the sample proportion of readmission?

b. Write the null and alternative hypotheses.

c. Find the value of the test statistic and explain it in context.

d. The p-value associated with this test statistic is 0.39. Explain the meaning of the p-value in this context. Based on this result, does the p-value indicate the null hypothesis should be doubted?