How do you find the 95 confidence interval for the mean?
The critical value for a 95% confidence interval is 1.96, where (1-0.95)/2 = 0.025. A 95% confidence interval for the unknown mean is ((101.82 – (1.96*0.49)), (101.82 + (1.96*0.49))) = (101.82 – 0.96, 101.82 + 0.96) = (100.86, 102.78).
What is the formula for confidence interval for the mean of a normal population?
If you don’t know your population mean (μ) but you do know the standard deviation (σ), you can find a confidence interval for the population mean, with the formula: x̄ ± z* σ / (√n), Step 1: Subtract the confidence level (Given as 95 percent in the question) from 1 and then divide the result by two.
How do you find the 95 confidence interval for the mean and standard deviation?
- Because you want a 95 percent confidence interval, your z*-value is 1.96.
- Suppose you take a random sample of 100 fingerlings and determine that the average length is 7.5 inches; assume the population standard deviation is 2.3 inches.
- Multiply 1.96 times 2.3 divided by the square root of 100 (which is 10).
How do you find the margin of error for a 98 confidence interval?
The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. This chart can be expanded to other confidence percentages as well….How to Calculate the Margin of Error for a Sample Mean.
| Percentage Confidence | z*-Value |
|---|---|
| 95 | 1.96 |
| 98 | 2.33 |
| 99 | 2.58 |
What is the 98% confidence level?
Z-values for Confidence Intervals
| Confidence Level | Z Value |
|---|---|
| 90% | 1.645 |
| 95% | 1.960 |
| 98% | 2.326 |
| 99% | 2.576 |
What does it mean to be 98% confidence?
The confidence interval includes 98 % of all possible values for the parameter. The probability that the value of the parameter lies between the lower and upper bounds of the interval is 98 %. The probability that it does not is 2 %.