Confidence Interval Statistics Example 1

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

Example 1

hard
A sample of 100 students has a mean test score of xห‰=72\bar{x} = 72 with population standard deviation ฯƒ=10\sigma = 10. Construct a 95% confidence interval for the population mean.

Solution

  1. 1
    Step 1: For 95% confidence, zโˆ—=1.96z^* = 1.96.
  2. 2
    Step 2: Standard error: SE=10100=1\text{SE} = \frac{10}{\sqrt{100}} = 1.
  3. 3
    Step 3: CI = xห‰ยฑzโˆ—โ‹…SE=72ยฑ1.96(1)=(70.04,73.96)\bar{x} \pm z^* \cdot \text{SE} = 72 \pm 1.96(1) = (70.04, 73.96).

Answer

(70.04,73.96)(70.04, 73.96)
A 95% confidence interval means that if we repeated this sampling process many times, about 95% of the intervals constructed would contain the true population mean.

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 โ†’

More Confidence Interval Examples

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]).

Example 4 hard

A 90% confidence interval for a population mean is given as 68 to 74. What are the sample mean and t

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