A 95% confidence interval obtained from a sample of 100 outpatients for the true

Question

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).

a. Provide a correct interpretation of this interval. Can you think of other interpretations that would also be correct?

b. 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?

c. If we wanted a 99% confidence interval instead, can you tell whether it would be narrower or wider? Can you tell by how much?

Explanation / Answer

a.) A 95% confidence interval for true population mean indicates that this interval or this range of values will have a probability of 0.95 of containing the true population mean.

The other interpretation that would be correct is - if repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the interval would contain the true population mean.

b.) No, it would not be same if we obtained a different set of 100 patients. Because those set of patients may have different mean and standard deviation

c.) A 99% confidence interval will be wider than a 95% confidence interval.

It will differe by 6.2

Reason suppose the mean is 100 and standard error 10 (say), and it remains same for both 95% and 99% confidence interval.

So, only the value of Zcritical will be different in the two cases and on calculation you will notice a difference of 6.2 between the two intervals.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.