Sample size is 24, Mean rate of 6.50%, Standard Deviation is 1.20. Calculate 90% of confidence interval
To calculate the 90% confidence interval with the given sample size, mean rate, and standard deviation, you can follow these steps:
1. Determine the critical value:
- The critical value is calculated based on the desired confidence level and the sample size.
- Since you want a 90% confidence interval, the remaining area outside the interval would be (100% - 90%)/2 = 5% on each tail.
- Look up the critical value for a 5% area in a standard normal distribution table or use a statistical calculator. The critical value for a 90% confidence level is approximately 1.645.
2. Calculate the standard error:
- The standard error is a measure of the uncertainty associated with the estimate of the population mean.
- Divide the standard deviation by the square root of the sample size.
- Standard error = standard deviation / sqrt(sample size)
- In this case, the standard error = 1.20 / sqrt(24).
3. Calculate the margin of error:
- The margin of error is the maximum amount by which the sample mean is likely to differ from the population mean.
- Multiply the critical value (from step 1) by the standard error (from step 2).
- Margin of error = critical value * standard error
4. Calculate the confidence interval:
- Subtract the margin of error (from step 3) from the sample mean to get the lower bound, and add it to the sample mean to get the upper bound.
- Confidence interval = sample mean ± margin of error
In the given example:
- Sample size (n) = 24
- Mean rate = 6.50%
- Standard deviation = 1.20
Now, let's calculate the 90% confidence interval.
Step 1: The critical value for a 90% confidence level is approximately 1.645.
Step 2: Calculate the standard error:
- Standard error = standard deviation / sqrt(sample size)
- Standard error = 1.20 / sqrt(24)
Step 3: Calculate the margin of error:
- Margin of error = critical value * standard error
Step 4: Calculate the confidence interval:
- Confidence interval = sample mean ± margin of error
By substituting the values into the formulas, you can calculate the confidence interval.