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What is Confidence interval?

An interval that estimates an unknown value, such as the population mean, from a sample with a range. A 95% confidence interval is made by a method such that, if sampling were repeated, about 95% of the resulting intervals would contain the true value. When the population standard deviation σ is known, the 95% confidence interval for the population mean is the sample mean ± 1.96 × σ/√n, where σ/√n is called the standard error. Making the sample size n four times as large halves the width of the interval.

Japanese name: 信頼区間

Confidence interval appears in 2 practice questions across 1 topic, including Probability, Statistics and Queueing.

Field: Probability, Statistics and Queueing

Try it: questions about Confidence interval

Which of the following correctly describes the meaning of a 95% confidence interval for the population mean obtained from a sample?

  1. AIt means that about 95% of the individual values in the population lie within the interval
  2. BIf samples were drawn again and intervals computed by the same method many times, about 95% of the intervals would contain the population mean
  3. CThe larger the sample, the more variation it contains, so the interval at the same confidence level becomes wider
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Answer: B. If samples were drawn again and intervals computed by the same method many times, about 95% of the intervals would contain the population mean

A confidence interval estimates an unknown value, such as the population mean, from a sample with a range. A 95% confidence interval is an interval made by a method such that, if sampling were repeated, about 95% of the resulting intervals would contain the true population mean. The width of the interval is proportional to the standard error σ/√n, so it narrows as the sample grows.

The standard deviation of a population is known to be 10. A sample of size 100 drawn from it has a sample mean of 50.0. Taking the two-sided 95% value of the standard normal distribution to be 1.96, which of the following is the 95% confidence interval for the population mean?

  1. A30.4 to 69.6
  2. B48.04 to 51.96
  3. C49.804 to 50.196
Show answer and explanation

Answer: B. 48.04 to 51.96

The standard error of the sample mean is 10 ÷ √100 = 1. The 95% confidence interval is "sample mean ± 1.96 × standard error", so 50.0 ± 1.96, which is 48.04 to 51.96. With a sample four times as large, 400, the half-width of the interval narrows to 1.96 × 10 ÷ 20 = 0.98.

Confidence interval in the explanations

Questions that mention Confidence interval (2)

  1. Which of the following correctly describes the meaning of a 95% confidence interval for the population mean obtained from a sample?
  2. The standard deviation of a population is known to be 10. A sample of size 100 drawn from it has a sample mean of 50.0. Taking the two-sided 95% value of the standard normal distribution to be 1.96, which of the following is the 95% confidence interval for the population mean?

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Related terms

Standard deviation Normal distribution Bayes' theorem Binomial distribution Conditional probability Correlation coefficient Expected value Exponential distribution Hypothesis testing Median

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