confidence interval

(noun)

A type of interval estimate of a population parameter used to indicate the reliability of an estimate.

Related Terms

Examples of confidence interval in the following topics:

  • Interpreting confidence intervals

    • A careful eye might have observed the somewhat awkward language used to describe confidence intervals.
    • Incorrect language might try to describe the confidence interval as capturing the population parameter with a certain probability.
    • Another especially important consideration of confidence intervals is that they only try to capture the population parameter.
    • Our intervals say nothing about the confidence of capturing individual observations, a proportion of the observations, or about capturing point estimates.
    • Confidence intervals only attempt to capture population parameters.

  • Level of Confidence

    • The proportion of confidence intervals that contain the true value of a parameter will match the confidence level.
    • This is guaranteed by the reasoning underlying the construction of confidence intervals.
    • Confidence intervals consist of a range of values (interval) that act as good estimates of the unknown population parameter .
    • This value is represented by a percentage, so when we say, "we are 99% confident that the true value of the parameter is in our confidence interval," we express that 99% of the observed confidence intervals will hold the true value of the parameter.
    • In applied practice, confidence intervals are typically stated at the 95% confidence level.

  • Lab 3: Confidence Interval (Womens' Heights)

    • The student will calculate a 90% confidence interval using the given data.
    • Now write your confidence interval on the board.
    • Divide this number by the total number of confidence intervals generated by the class to determine the percent of confidence intervals that contains the mean ยต.
    • Suppose we had generated 100 confidence intervals.
    • When we construct a 90% confidence interval, we say that we are 90% confident that the true population mean lies within the confidence interval.

  • Hypothesis Tests or Confidence Intervals?

    • Hypothesis tests and confidence intervals are related, but have some important differences.
    • What is the difference between hypothesis testing and confidence intervals?
    • When we use confidence intervals, we are estimating the parameters of interest.
    • Confidence intervals are closely related to statistical significance testing.
    • Explain how confidence intervals are used to estimate parameters of interest

  • Introduction to Confidence Intervals

    • State why a confidence interval is not the probability the interval contains the parameter
    • Confidence intervals provide more information than point estimates.
    • These intervals are referred to as 95% and 99% confidence intervals respectively.
    • An example of a 95% confidence interval is shown below:
    • Which procedure produces the "true" 95% confidence interval?

  • Working Backwards to Find the Error Bound or Sample Mean

    • When we calculate a confidence interval, we find the sample mean and calculate the error bound and use them to calculate the confidence interval.
    • But sometimes when we read statistical studies, the study may state the confidence interval only.
    • Subtract the error bound from the upper value of the confidence interval
    • OR, Average the upper and lower endpoints of the confidence interval
    • Suppose we know that a confidence interval is (67.18, 68.82) and we want to find the error bound.

  • Lab 2: Confidence Interval (Place of Birth)

    • The student will calculate the 90% confidence interval for proportion of students in this school that were born in this state.
    • The student will determine the effects that changing conditions have on the confidence interval.
    • Calculate the confidence interval and the error bound. i.
    • Using the above information, construct a confidence interval for each given confidence level given.
    • Does the width of the confidence interval increase or decrease?

  • Lab 1: Confidence Interval (Home Costs)

    • The student will determine the effects that changing conditions has on the confidence interval.
    • Calculate the confidence interval and the error bound. i.
    • Some students think that a 90% confidence interval contains 90% of the data.
    • Using the above information, construct a confidence interval for each confidence level given.
    • Does the width of the confidence interval increase or decrease?

  • Changing the Confidence Level or Sample Size

    • The 90% confidence interval is (67.18, 68.82).
    • The 95% confidence interval is (67.02, 68.98).
    • The 95% confidence interval is wider.
    • Increasing the confidence level increases the error bound, making the confidence interval wider.
    • Decreasing the confidence level decreases the error bound, making the confidence interval narrower.

  • Confidence Intervals

    • These sections show how to compute confidence intervals for a variety of parameters.