Confidence Interval Statistics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A 90% confidence interval for a population mean is given as 68 to 74. What are the sample mean and the margin of error?

Solution

  1. 1
    Step 1: The sample mean is the midpoint of the interval: 68+742=71\frac{68+74}{2} = 71.
  2. 2
    Step 2: The margin of error is half the width: 74−682=3\frac{74-68}{2} = 3.

Answer

Sample mean = 7171 and margin of error = 33.
Confidence intervals are built from a center and a margin of error. Reading these parts from an interval helps connect the visual interval to the underlying estimation process.

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 →

More Confidence Interval Examples

Example 1 hard

A sample of 100 students has a mean test score of [formula] with population standard deviation [form

Example 2 hard

A 95% confidence interval for the mean weight of apples is (150g, 170g). Interpret this interval.

Example 3 hard

A sample of 64 has [formula] and [formula]. Find the 99% confidence interval ([formula]).

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