A newspaper article states with 95% confidence that 58% to 62% of all high school juniors and seniors in the United States claim that they have missed their first class of the day because the school day starts too early. This confidence interval is based on a poll of 2000 high school students in Detroit.
How would you interpret the confidence interval from this newspaper article?
A.
If we took many samples of high school students from different urban cities, 95% of the samples would have between 58% and 62% high school students who miss the first class of their day
B.
95% of large urban cities in the United States have 58% to 62% high school students who miss their first class of the day
C.
We can be 95% confident that between 58% and 62% of all United States high school students would miss their first class of the day
D.
You cannot use this confidence interval to generalize to all teenagers in the United States because of the way the sample was taken
A. If we took many samples of high school students from different urban cities, 95% of the samples would have between 58% and 62% high school students who miss the first class of their day
C. We can be 95% confident that between 58% and 62% of all United States high school students would miss their first class of the day.
The correct interpretation of the confidence interval from this newspaper article would be:
C. We can be 95% confident that between 58% and 62% of all United States high school students would miss their first class of the day.
Explanation:
The article states that the confidence interval is based on a poll of 2000 high school students in Detroit. However, it doesn't necessarily mean that the entire high school population in the United States was surveyed. Instead, the sample surveyed includes high school students from Detroit. Therefore, we cannot generalize the results to all high school students in the United States with absolute certainty.
However, with a 95% confidence level, we can be reasonably confident that the true proportion of high school students in the United States who miss their first class of the day falls within the range of 58% to 62%. This means that if we were to repeat the sampling process many times and calculate the confidence interval each time, about 95% of those intervals would contain the true proportion of high school students who miss their first class. Therefore, we can conclude that we are 95% confident in the estimate provided by the confidence interval.