Content

• Steps
• Advice
• What you need

Confidence interval is an indicator that helps us to know the accuracy of a measurement. In addition, the confidence interval also indicates stability when estimating a value, i.e. thanks to the confidence interval, you can see how the results of the repeatable measurement will deviate from the original estimate. . The following article will help you learn how to calculate confidence intervals.

Steps

1. 

   Note the phenomenon you want to check. Let's say you want to test the following scenario: Average weight of male students at ABC school is 81 kg (equivalent to 180 lbs).. You need to check if your prediction about the weight of male students in ABC is correct within a given confidence interval.

2. 

   
   
   Select a sample from a given population. This is the step you will take to collect data to test your hypothesis. Let's say you have randomly selected 1000 male students.

3. 

   Calculate the mean and standard deviation of the sample. Select a sample statistical value (eg sample mean, sample standard deviation) that you want to use to estimate your chosen population parameter. A population parameter is a value that represents a certain characteristic of that population. To calculate the mean and standard deviation of the sample, do the following:
   • We calculate the mean by taking the sum of the weights of the 1000 selected male students and dividing the total obtained by 1000, that is, the number of students. The average weight obtained will be 81 kg (180 lbs).
   • To calculate the standard deviation, you need to determine the mean of the set of data. Then, you need to calculate the variability of the data, or in other words find the mean of the squared deviation from the mean. Next, we will get the square root of the obtained value. Assume the calculated standard deviation is 14 kg (equivalent to 30 lbs). (Note: sometimes a standard deviation value will be given in statistical problems.)

4. 

   
   
   Choose your desired confidence interval. The commonly used confidence intervals are 90%, 95%, and 99%. This value is also usually given. For example consider the 95% confidence interval.

5. 

   Calculate the range of error or limit of error. The limit of error can be calculated by the formula: Z_{a / 2} * σ / √ (n). In there, Z_{a / 2} is the confidence factor, where a is the confidence interval, is the standard deviation, and n is the sample size. In other words, you need to multiply the limit value by the standard error. To solve this formula, divide the formula into the following parts:
   • To calculate the limit value Z_{a / 2}: Confidence interval under consideration is 95%. Converting from a percent to a decimal value gives: 0.95; divide this value by 2 to get 0.475. Next, compare with the z table to find the corresponding value 0.475. We see that the closest value of 1.96 lies at the intersection of row 1.9 and column 0.06.
   • To calculate the standard error, take the standard deviation of 30 (in lbs, and 14 in kg), and divide this value by the square root of the sample size of 1000. You get 30 / 31.6 = 0.95 lbs, or (14 / 31.6 = 0.44 kg).
   • Multiply the critical value by the standard error, i.e. take 1.96 x 0.95 = 1.86 (in lbs) or 1.96 x 0.44 = 0.86 (in kg). This product is the limit of error or the range of error.

6. 

   
   
   Record the confidence interval. To record the confidence interval, take the mean (180 lbs, or 81 kg) and write it to the left of the ± sign then to the limit of error. So, the result is: 180 ± 1.86 lbs or 81 ± 0.44 kg. We can determine the upper and lower bound of the confidence interval by adding or subtracting the mean value by the range of error. That is, if expressed in lbs, the lower bound is 180 - 1.86 = 178.16 and the upper bound is 180 + 1.86 = 181.86.
   • We can also use this formula to determine the confidence interval: x̅ ± Z_{a / 2} * σ / √ (n). Where x̅ is the mean.
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Advice

• It is possible to compute t-values ​​and z-values ​​by hand or using a calculator with graphs or statistics tables that are usually included in the statistics book. The z-value can be determined using the Standard Distribution Calculator, while the t-value can be calculated using the t-Distribution Calculator. In addition, you can also use support tools available online.
• The size of the sample should be large enough for the confidence interval to be valid.
• The critical value used to calculate the range of error is a constant and is expressed as a t-value or z-statistic. A t-value is often used when the population standard deviation is unknown or when the sample size is not large enough.
• There are several sampling methods that can help you choose a representative sample for the test, such as simple random sampling, systematic sampling or stratified sampling.
• Confidence intervals do not indicate the probability of a single outcome. For example, with a 95% confidence interval, you could say that the population mean is between 75 and 100. The 95% confidence interval does not mean you can be 95% sure that the value is The average of the test will fall within the range of the value you calculated.

What you need

• A sample set
• Computer
• Network connections
• Textbook of statistics
• Handheld computer with graphics