QQuestionStatistics
QuestionStatistics
What does the 95% represent in a 95% confidence interval?
Choose the correct answer below:
A. The 95% represents the probability the interval will contain the parameter (for example, the population mean or population proportion).
B. The 95% represents the proportion of intervals that will not contain the parameter (for example, the population mean or population proportion) if a large number of different samples is obtained.
C. The 98% represents the probability the interval will not contain the parameter (for example, the population mean or population proportion).
D. The 95% represents the proportion of intervals that would contain the parameter (for example, the population mean or population proportion) if a large number of different samples is obtained.
10 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:Let me solve this step by step with a clear explanation of confidence intervals.
Step 2:: Understanding Confidence Intervals
A confidence interval is a range of values that is likely to contain an unknown population parameter with a certain level of confidence. In this case, we're discussing a 95% confidence interval.
Step 3:: Interpreting the 95% Confidence Level
The 95% represents the probability that if we were to repeatedly take many different samples from the same population and construct confidence intervals, approximately 95% of those intervals would contain the true population parameter.
Step 4:: Breaking Down the Interpretation
- This means that if we repeated the sampling process many times, about 95 out of 100 constructed intervals would include the true population parameter (such as the population mean or proportion). - It does NOT mean that there is a 95% chance that the specific interval we've calculated contains the parameter.
Step 5:: Evaluating the Given Options
Looking at the options, the description in option D most accurately captures this concept: "The 95% represents the proportion of intervals that would contain the parameter (for example, the population mean or population proportion) if a large number of different samples is obtained."
Final Answer
The 95% in a 95% confidence interval represents the proportion of intervals that would contain the true population parameter if many different samples were drawn and intervals constructed. Key Insights: - Confidence intervals provide a range of plausible values for a population parameter - The percentage (95%) indicates the long-run reliability of the interval construction method - It does not mean there's a 95% chance the specific interval contains the parameter
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students