Confidence Interval Statistics Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardA 95% confidence interval for the mean weight of apples is (150g, 170g). Interpret this interval.
Solution
- 1 Step 1: The interval estimates that the true population mean weight is between 150g and 170g.
- 2 Step 2: We are 95% confident in this interval, meaning if we repeated the process many times, 95% of intervals would capture the true mean.
- 3 Step 3: It does NOT mean there is a 95% probability that is in this specific interval โ is fixed.
Answer
We are 95% confident that the true mean weight of apples lies between 150g and 170g.
Correct interpretation of confidence intervals is crucial. The confidence level refers to the long-run success rate of the method, not the probability for a single interval.
About Confidence Interval
A confidence interval is a range of values, calculated from sample data, constructed so that the procedure captures the true population parameter a specified percentage of the time (e.g., 95%). It quantifies the uncertainty inherent in using a sample to estimate a population value.
Learn more about Confidence Interval โMore Confidence Interval Examples
Example 1 hard
A sample of 100 students has a mean test score of [formula] with population standard deviation [form
Example 3 hardA sample of 64 has [formula] and [formula]. Find the 99% confidence interval ([formula]).
Example 4 hardA 90% confidence interval for a population mean is given as 68 to 74. What are the sample mean and t