Math  /  Data & Statistics

QuestionA hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain time period. Nationally the readmission rate for patients with pneumonia is 19%19 \%. A hospital was interested in knowing whether their readmission rate for preumonia was less than the national percentage. They found 9 patients out of 60 treated for pneumonia in a two-month period were readmitted. Complete parts (a) through (d) below. c. Find the value of the test statistic and explain it in context.
The test statistic is \square (Type an integer or a decimal rounded to two decimal places as needed.) The value of the test statistic tells that the observed proportion of readmissions was \square \square \square the null hypothesis proportion of readmissions. (Type an integer or a decimal rounded to two decimal places as needed.) d. The p-value associated with this test statistic is 0.21 . Explain the meaning of the pp-value in this context. Based on this result, does the p-value indicate the null hypothesis should be doubted? Select the correct choice below and fill in the answer box within your choice. (Type an integer or a decimal. Do not round.) A. The probability of getting 9 or fewer readmissions for pneumonia of a random sample of 60 patients with preumonia is \square . assuming the population proportion is less than 0.19. B. The probability of getting 9 or fewer readmissions for pneumonia of a random sample of 60 patients with pneumonia is \qquad , assuming the population proportion is 0.19.

Studdy Solution
The test statistic is 0.79-0.79.
The value of the test statistic tells us that the observed proportion of readmissions was 0.790.79 standard deviations *below* the null hypothesis proportion of readmissions.
The correct choice is B: The probability of getting 9 or fewer readmissions for pneumonia out of a random sample of 60 patients with pneumonia is 0.210.21, assuming the population proportion is 0.190.19.

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