Step by step process in calculation of confidence limit ?

1. Determine the sample mean and sample standard deviation of the data set.

2. Decide on the confidence level you want to use. Common confidence levels are 90%, 95%, and 99%.

3. Look up the critical value for the desired confidence level in a t-distribution table. The critical value is based on the degrees of freedom, which is equal to the sample size minus 1.

4. Calculate the margin of error by multiplying the critical value by the standard error of the mean. The standard error of the mean is equal to the sample standard deviation divided by the square root of the sample size.

5. Calculate the lower confidence limit by subtracting the margin of error from the sample mean.

6. Calculate the upper confidence limit by adding the margin of error to the sample mean.

7. The confidence interval is the range between the lower and upper confidence limits. It represents the range within which the true population mean is likely to fall with the chosen level of confidence.

Step 1: Determine the Sample Size (n)

- Calculate the sample size using a confidence interval formula or sample size calculator.

Step 2: Calculate the Sample Mean (x̄)

- Sum all the values in the sample and divide by the sample size.

Step 3: Estimate the Population Standard Deviation (s)

- Calculate the sample standard deviation using the following formula:
```
s = √[ Σ (x - x̄)² / (n - 1) ]
```

Step 4: Determine the Confidence Level

- Choose the desired confidence level, typically 90%, 95%, or 99%.

Step 5: Calculate the Critical Value (z)

- Using the confidence level, find the corresponding critical value (z) from a standard normal distribution table.

Step 6: Calculate the Confidence Interval

- Calculate the confidence interval using the following formula:
```
x̄ ± z - (s / √n)
```

Step 7: Interpret the Confidence Limit

- The confidence interval represents a range of values that is likely to include the true population mean with the specified confidence level.
- If the true population mean falls within the confidence interval, it is considered statistically significant at the specified confidence level.