Confidence intervals (CIs) are a fundamental concept in statistics that provide a range of values within which we can expect a population parameter to fall, with a certain level of confidence. Understanding how to interpret these intervals is crucial for making informed decisions based on data. Below are three diverse and practical examples of confidence interval interpretation.
In a recent customer satisfaction survey conducted by a retail company, 200 customers were randomly selected to provide feedback on their shopping experience. The survey revealed that 75% of respondents rated their experience as satisfactory. To gauge the reliability of this finding, the company calculates a 95% confidence interval for the proportion of all customers who are satisfied.
The calculation yields a confidence interval of 70% to 80%. This means that the company can be 95% confident that the true percentage of all customers who are satisfied lies between 70% and 80%.
Notes: This type of confidence interval helps the company understand the range of customer satisfaction in the broader population, guiding decisions on potential improvements.
A health researcher is interested in understanding the average height of adult males in a specific city. She randomly selects a sample of 150 adult males and measures their heights. The calculated sample mean height is 175 cm, with a standard deviation of 10 cm. Using this data, she constructs a 95% confidence interval for the average height of adult males in the city.
The resulting confidence interval is 173 cm to 177 cm. This indicates that the researcher can be 95% confident that the true average height of all adult males in the city falls within this range.
Notes: This example illustrates how confidence intervals can provide insights into population parameters, helping to inform urban health policies and planning.
An educational researcher wants to evaluate the effectiveness of a new teaching method on student performance. She administers a standardized test to a sample of 100 students taught using the new method, resulting in an average score of 82 with a standard deviation of 5. To assess the reliability of these results, she calculates a 90% confidence interval for the average test score.
The confidence interval is determined to be 81 cm to 83 cm. This implies that the researcher can be 90% confident that the true average test score of all students taught with this method is between 81 and 83.
Notes: This analysis helps in understanding the impact of teaching methods on student performance, guiding future instructional strategies.