Math Problem Statement

Which of the following selections illustrates the proper form for a 95% confidence interval summary statement?

Solution

The question asks for the proper form for a 95% confidence interval summary statement. Let's analyze the choices:

  • Option A: "We are 95% confident that, in the sample, the mean SITA score is between 25.7 and 29.8 points."

    • This is incorrect because a confidence interval refers to a population parameter, not a sample statistic.
  • Option B: "We are 95% confident that, in the population, the mean SITA score is between 25.7 and 29.8 points."

    • This is correct. Confidence intervals are used to estimate population parameters, and this statement correctly reflects that interpretation.
  • Option C: "We are confident that the mean SITA score is between 25.7 and 29.8 points."

    • This omits the 95% confidence level, making it incomplete and incorrect.
  • Option D: "We are confident that 95% of the sample scored between 25.7 and 29.8 points."

    • This is incorrect because confidence intervals refer to population means, not to individual scores within the sample.

The correct answer is B.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. What is a confidence interval, and how is it interpreted?
  2. How do you calculate a 95% confidence interval for the mean?
  3. What does "95% confidence" actually mean in statistical terms?
  4. What happens to the confidence interval if you increase the confidence level to 99%?
  5. How does sample size affect the width of a confidence interval?

Tip: A larger sample size will result in a narrower confidence interval, giving a more precise estimate of the population parameter.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals

Formulas

-

Theorems

Confidence Interval Theorem

Suitable Grade Level

Undergraduate