Create a response to the classmates post.
Initial discussion question: The focus this week is on confidence intervals. Utilize the following information and answer the questions below. A 95% confidence interval obtained from a sample of 100 outpatients for the true population mean normal mean systolic blood pressure is given by (114 mmHG, 120 mmHG).
Provide a correct interpretation of this interval. Can you think of other interpretations that would also be correct?
This confidence interval came from a single sample, would we get the same interval if we obtained a different set of 100 patients? What does this imply about your interpretation of the given interval?
If we wanted a 99% confidence interval instead, can you tell whether it would be narrower or wider? Can you tell by how much?
Classmate post: Interpretation of this interval:
We are 95% confident that the true mean systolic blood pressure for the population from which these people came from is between 114mmHG and 120mmHG.
Other possible interpretations?
There is only a 5% chance that the range of 114mmHG and 120mmHG excludes the mean systolic blood pressure for the population from which these people come from.
Would we get the same interval if we obtained a different set of 100 patients? What does this imply about your interpretation of the given interval?
No, the population parameter is determined by the specific sample. If we obtained a different sample of the same sample size we would still get a different sample mean and a different confidence interval. In a 95% confidence interval, we can expect that 95 out of 100 samples will have a population parameter that lies within the estimated 95% confidence interval.
If we wanted a 99% confidence interval instead, can you tell whether it would be narrower or wider? Can you tell by how much?
The 99% confidence interval would be wider than the 95% confidence interval. This is because to be more confident that the true population value falls within the interval we will need to allow more potential values within the interval. As a general rule: The higher the degree of confidence that the interval will include the true population value, the wider the confidence level is needed.
