wait times a hospital claims that 75% of people who come to its emergency room are seen by a doctor within 30 minutes of checking in. to verify this claim, an auditor inspects the medical records of 55 randomly selected patients who checked into the emergency room during the last year. only 32 (58.2%) of these patients were seen by a doctor within 30 minutes of checking in. if the wait time is less than 30 minutes for 75% of all patients in the emergency room, what is the probability that the proportion of patients who wait less than 30 minutes is 0.582 or less in a random sample of 55 patients? based on your answer to part (a), is there convincing evidence that less than 75% of all patients in the emergency room wait less than 30 minutes? explain your reasoning.

proportionof 0.582 is statistically significantly lower than theclaimedproportion of 0.75, which means there is no convincing evidence that less than 75% of all patients in theemergency roomwait less than 30 minutes## How to determine if there is convincing evidence that less than 75% of all patients in the emergency room wait less than 30 minutes?

proportionof patients waiting less than 30 minutes as low as 0.582 or lower if the true proportion of patients waiting less than 30 minutes was really 75%.z-testfor proportions. The null hypothesis for this test is that the true proportion of patients waiting less than 30 minutes is equal to the claimed proportion of 75%, while the alternative hypothesis is that the true proportion is less than 75%.observedproportion –claimedproportion) / standard errorprobabilityis known as the p-value. A p-value less than 0.05 is often considered to be statistically significant and indicates that the observed difference is unlikely to be due to random chance.emergency roomis less than 75%.z-teston: