The mean age of the 43 presidents of the United States (as of 2011) on the day of inauguration is 54.6 years, with a standard deviation of 6.3 years. A researcher constructed a 95% confidence interval for the mean age of presidents on inauguration day. He wrote that he was 95% confident that the mean age of the president on inauguration day is between 52.7 and 56.5 years of age. What is wrong to the researcher's approach to data analysis?
**i dont understand this question. Any help?
95% = mean ± Z(SEm)
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (±.475) and its Z score. Insert Z and other data into above equations to check.
Certainly! This question is asking you to identify what is wrong with the researcher's approach to data analysis regarding the construction of a confidence interval for the mean age of presidents on inauguration day.
To begin, let's understand the concept of a confidence interval. A confidence interval is a range of values (in this case, ages) that is likely to contain the true population mean with a certain level of confidence. In this case, the researcher claims to have constructed a 95% confidence interval for the mean age of presidents.
Now, the problem lies in the researcher's statement, which asserts that they are "95% confident that the mean age of the president on inauguration day is between 52.7 and 56.5 years of age." This statement is incorrect and displays a misunderstanding of what a confidence interval represents.
A 95% confidence interval does not mean that the true population mean (mean age of all presidents) falls within the interval with 95% certainty. Rather, it means that if the researcher were to conduct multiple samples and calculate confidence intervals using the same method, approximately 95% of these intervals would contain the true population mean.
In other words, the confidence interval provides a range of plausible values for the mean age of presidents, not a specific range that contains the mean with 95% certainty. Therefore, the researcher's claim of confidence in their interval is incorrect.