Chapter 8, Problem 21SE

Hospital Readmission 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 $\hat{p}$, 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 $\mathrm{0.39.}$ 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?