A researcher collected data on the annual salary of doctors in Nova Scotia.He wishes to construct a confidence interval for the mean annual salary.Which of the following is/are true?
I.A 98% confidence interval will have a greater chance of including the true mean salary than a 95% confidence interval.
II.A 98% confidence interval will be narrower than a 95% confidence interval.
III.A 98% confidence interval requires the researcher to take a larger sample.

Question

A researcher collected data on the annual salary of doctors in Nova Scotia.He wishes to construct a confidence interval for the mean annual salary.Which of the following is/are true? 
I.A 98% confidence interval will have a greater chance of including the true mean salary than a 95% confidence interval.
II.A 98% confidence interval will be narrower than a 95% confidence interval.
III.A 98% confidence interval requires the researcher to take a larger sample.

Quizplus · Accepted Answer

I is true because a higher confidence level (98% vs. 95%) means there is a greater chance of the interval including the true mean, as it will be wider to cover more possibilities. II is incorrect because a 98% confidence interval will be wider, not narrower, than a 95% confidence interval, to ensure a higher confidence of including the true mean. III is incorrect because the size of the confidence interval is not directly determined by the sample size but by the confidence level and the variability in the data; a larger sample can reduce the width of the confidence interval but is not a requirement for achieving a specific confidence level.

A Researcher Collected Data on the Annual Salary of Doctors