Answer :
To understand which statements about the given confidence interval are correct, let's break down what a 90% confidence interval (CI) means:
90% of patients who have this surgery have a recovery time between 92.2 and 97.8 days.
This statement is incorrect. The confidence interval refers to the mean recovery time, not the individual recovery times of the patients.
If many more samples were drawn and confidence intervals were created for each one, then 90% of those intervals would contain the true mean recovery time for patients who have this surgery.
This statement is correct. The essence of a confidence interval is that if we were to take many samples and compute a confidence interval for each one, approximately 90% of those intervals would capture the true population mean.
We are 90% confident that the mean recovery time of the 245 patients in this sample is between 92.2 and 97.8 days.
This statement is incorrect. The confidence interval is an estimate for the population mean, not the sample mean. The sample mean is a single observed value.
If one patient who has this surgery is randomly chosen, there is a 90% probability that their recovery time will be between 92.2 and 97.8 days.
This statement is incorrect. The confidence interval pertains to the mean recovery time, not individual recovery times. Individual recovery times can vary widely around the mean.
90% of patients who have this surgery fully recover.
This statement is incorrect. The confidence interval gives no information about the proportion of patients who fully recover; it only pertains to the mean recovery time.
We are 90% confident that the mean recovery time for all patients who have this surgery is between 92.2 and 97.8 days.
This statement is correct. The confidence interval is an estimate, based on the sample data, of where the true population mean for all patients who undergo this surgery would lie.
In conclusion, the correct statements about this confidence interval are statements 2 and 6.