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The confidence interval is a measure of the measurement accuracy. It is also an indicator of how stable the obtained value is, that is, how close the value (to the original value) you get when you repeat the measurements (experiment). Follow these steps to calculate the confidence interval for the values ​​you want.

Steps

1. 1 Write down the task. For example: the average weight of a male student at ABC University is 90 kg... You will test the accuracy of predicting the weight of male students at ABC University within a given confidence interval.
2. 2 Make a suitable sample. You will use it to collect data to test your hypothesis. Let's say you've already randomly selected 1000 male students.
3. 3 Calculate the mean and standard deviation of this sample. Select the statistical quantities (for example, mean and standard deviation) that you want to use to analyze your sample. Here's how to calculate the mean and standard deviation:
   • To calculate the sample mean, add the weights of the 1,000 selected males and divide the result by 1,000 (the number of males). Let's say you got an average weight of 93 kg.
   • To calculate the standard deviation of the sample, you need to find the mean. Then you need to calculate the variance of the data, or the mean of the squared differences from the mean. When you find this number, just take the square root of it. Let's say, in our example, the standard deviation is 15 kg (note that sometimes this information can be given together with the condition of the statistical problem).
4. 4 Select the desired confidence level. The most commonly used confidence levels are 90%, 95%, and 99%. It can also be given along with the problem statement. Let's say you chose 95%.
5. 5 Calculate the margin of error. You can find the margin of error using the following formula: Z_{a / 2} * σ / √ (n). Z_{a / 2} = coefficient of confidence (where a = confidence level), σ = standard deviation, and n = sample size. This formula indicates that you must multiply the critical value by the standard error. Here's how you can solve this formula by breaking it down into parts:
   • Calculate the critical value or Z_{a / 2}... The confidence level is 95%. Convert percentages to decimal: 0.95 and divide by 2 to get 0.475. Then look at the Z-score table to find the corresponding value for 0.475. You will find the value 1.96 (at the intersection of row 1.9 and column 0.06).
   • Take the standard error (standard deviation): 15 and divide by the square root of the sample size: 1000. You get: 15 / 31.6 or 0.47 kg.
   • Multiply 1.96 by 0.47 (critical value by standard error) to get 0.92, the margin of error.
6. 6 Write down the confidence interval. To formulate the confidence interval, simply write down the mean (93) ± error. Answer: 93 ± 0.92. You can find the upper and lower bounds of the confidence interval by adding and subtracting the uncertainty to / from the mean. So, the lower limit is 93 - 0.92 or 92.08, and the upper limit is 93 + 0.92 or 93.92.
   • You can use the following formula to calculate the confidence interval: x̅ ± Z_{a / 2} * σ / √ (n), where x̅ is the mean value.

Tips

• Both t-scores and z-scores can be calculated manually, as well as using a graphing calculator or statistical tables, which are often found in statistics textbooks. Online tools are also available.
• The critical value used to calculate the uncertainty is constant and is expressed in either a t-score or a z-score. The T-score is generally preferred in settings where the sample standard deviation is unknown or when a small sample is used.
• Your sample must be large enough to calculate the correct confidence interval.
• The confidence interval does not indicate the likelihood of obtaining a particular result. For example, if you are 95% sure that the mean of your sample is between 75 and 100, then a 95% confidence interval does not mean that the mean is within your range.
• There are many methods, such as simple random sampling, systematic sampling, and stratified sampling, with which you can collect a representative sample for testing.

What do you need

• Sample
• Computer
• Access to the Internet
• Statistics tutorial
• Graphing calculator