Question

A hospital administrator hoping to improve wait times decides to estimate the average emergency room waiting time at her hospital. She collects a simple random sample of 64 patients and determines the time (in minutes) between when they checked in to the ER until they were first seen by a doctor. A 95% confidence interval based on this sample is (128 minutes, 147 minutes), which is based on the normal model for the mean.

Determine if the following statement is true.

a. 95% of random samples have a sample mean between 128 and 147 minutes.

b. A 99% confidence interval would be narrower than the 95% confidence interval since we need to be more sure of our estimate.

c. In order to decrease the margin of error of a 95% confidence interval to half of what it is now, we would need to double the sample size (Hint: the margin of error for a mean scales in the same way with sample size as the margin of error for a proportion)

Answer 1

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