Compare the precision of each indicator (1 vs 2, 2 vs 3, 1 vs 3) at a 95% confidence level.
Understand the Problem
The question asks to compare the precision of three different indicators (Bromothymol blue, Methyl red, and Bromocresol green) used in a titration experiment to determine the concentration of HCl. The precision should be compared pairwise (1 vs 2, 2 vs 3, and 1 vs 3) at a 95% confidence level, considering the mean HCl concentration, standard deviation, and number of measurements for each indicator.
Answer
Comparing the standard deviations: Methyl Red is more precise than both Bromothymol Blue and Bromocresol Green. Bromocresol Green is more precise than Bromothymol Blue.
Here's a comparison of the precision for each indicator pair at a 95% confidence level:
- 1 vs 2: Methyl Red (2) is more precise than Bromothymol Blue (1) because 0.00098 < 0.00225.
- 2 vs 3: Methyl Red (2) is more precise than Bromocresol Green (3) because 0.00098 < 0.00113.
- 1 vs 3: Bromocresol Green (3) is more precise than Bromothymol Blue (1) because 0.00113 < 0.00225.
Answer for screen readers
Here's a comparison of the precision for each indicator pair at a 95% confidence level:
- 1 vs 2: Methyl Red (2) is more precise than Bromothymol Blue (1) because 0.00098 < 0.00225.
- 2 vs 3: Methyl Red (2) is more precise than Bromocresol Green (3) because 0.00098 < 0.00113.
- 1 vs 3: Bromocresol Green (3) is more precise than Bromothymol Blue (1) because 0.00113 < 0.00225.
More Information
A 95% confidence level means that if the same population were sampled multiple times, approximately 95% of the resulting confidence intervals would contain the true population parameter.
Tips
A common mistake is to confuse standard deviation with the confidence interval. The standard deviation describes the spread of individual data points, while the confidence interval estimates a range for the population mean.
Sources
- Using Confidence Intervals to Compare Means - Statistics By Jim - statisticsbyjim.com
- Confidence interval - Biochemia Medica - biochemia-medica.com
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