How to find confidence intervals for a mean
Practice Questions
AP Statistics › How to find confidence intervals for a mean
An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500.
Provide a 98% confidence interval for the true mean cost of repair.
The population standard deviation is 7. Our sample size is 36.
What is the 95% margin of error for:
-
the population mean
-
the sample mean
A sample of 
Find the 
300 hundred eggs were randomly chosen from a gravid female salmon and individually weighed. The mean weight was 0.978 g with a standard deviation of 0.042. Find the 95% confidence interval for the mean weight of the salmon eggs (because it is a large n, use the standard normal distribution).
| Subject | Horn Length (in) | Subject | Horn Length (in) |
|---|---|---|---|
| 1 | 19.1 | 11 | 11.6 |
| 2 | 14.7 | 12 | 18.5 |
| 3 | 10.2 | 13 | 28.7 |
| 4 | 16.1 | 14 | 15.3 |
| 5 | 13.9 | 15 | 13.5 |
| 6 | 12.0 | 16 | 7.7 |
| 7 | 20.7 | 17 | 17.2 |
| 8 | 8.6 | 18 | 19.0 |
| 9 | 24.2 | 19 | 20.9 |
| 10 | 17.3 | 20 | 21.3 |
The data above represents measurements of the horn lengths of African water buffalo that were raised on calcium supplements. Construct a 95% confidence interval for the population mean for horn length after supplments.
Suppose you have a normally distributed variable with known variance. How many standard errors do you need to add and subtract from the sample mean so that you obtain 95% confidence intervals?