Confidence Interval Statistics Example 3

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Example 3

hard
A sample of 64 has xห‰=50\bar{x} = 50 and ฯƒ=8\sigma = 8. Find the 99% confidence interval (zโˆ—=2.576z^* = 2.576).

Solution

  1. 1
    Step 1: SE = 864=1\frac{8}{\sqrt{64}} = 1. Margin of error = 2.576ร—1=2.5762.576 \times 1 = 2.576.
  2. 2
    Step 2: CI = 50ยฑ2.576=(47.42,52.58)50 \pm 2.576 = (47.42, 52.58).

Answer

(47.42,52.58)(47.42, 52.58)
A 99% confidence interval is wider than a 95% interval because greater confidence requires a larger margin of error.

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 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 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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