Question

The proportion of patients who visit the emergency room (ER) and die within the year is 0.05. Suppose a hospital administrator is concerned that his ER has a higher proportion of patients who die within the year. In a random sample of 250 patients who have visited the ER in the past year, 17 have died. Should the administrator be concerned? Complete parts (a) through (g) below. (a) What are the null and alternative hypotheses? H0: p = 0.05 H1: p > 0.05 (b) Verify the requirements that allow use of the normal model to test the hypothesis are satisfied. Assume the size of the population is over 10,000 individuals. np0(1-p0) > 10 (c) Determine the sample proportion, p. p = 17/250 = 0.068 (d) Determine the test statistic, z0. z0 = (p - p0) / sqrt(p0(1-p0)/n) = (0.068 - 0.05) / sqrt(0.05(1-0.05)/250) = 1.31 (e) Determine the P-value. P-value = P(Z > 1.31) = 0.095 (f) Interpret the P-value. If the hospital administrator conducted this study 100 different times and the population proportion of patients who visit the ER and die within the year is 0.05, the administrator would expect 9.5 of the studies to result in a sample proportion of 0.068 or higher. (g) State your conclusion. There is sufficient evidence at alpha equals 0.10, but not at alpha equals 0.05 or alpha equals 0.01 to conclude the proportion of patients who visit the ER and die within the year is greater than 0.05.

          The proportion of patients who visit the emergency room (ER) and die within the year is 0.05. Suppose a hospital administrator is concerned that his ER has a higher proportion of patients who die within the year. In a random sample of 250 patients who have visited the ER in the past year, 17 have died. Should the administrator be concerned? Complete parts (a) through (g) below.

(a) What are the null and alternative hypotheses?
H0: p = 0.05
H1: p > 0.05

(b) Verify the requirements that allow use of the normal model to test the hypothesis are satisfied. Assume the size of the population is over 10,000 individuals.
np0(1-p0) > 10

(c) Determine the sample proportion, p.
p = 17/250 = 0.068

(d) Determine the test statistic, z0.
z0 = (p - p0) / sqrt(p0(1-p0)/n) = (0.068 - 0.05) / sqrt(0.05(1-0.05)/250) = 1.31

(e) Determine the P-value.
P-value = P(Z > 1.31) = 0.095

(f) Interpret the P-value.
If the hospital administrator conducted this study 100 different times and the population proportion of patients who visit the ER and die within the year is 0.05, the administrator would expect 9.5 of the studies to result in a sample proportion of 0.068 or higher.

(g) State your conclusion.
There is sufficient evidence at alpha equals 0.10, but not at alpha equals 0.05 or alpha equals 0.01 to conclude the proportion of patients who visit the ER and die within the year is greater than 0.05.

Added by Joshua C.

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