bounded interval

(noun)

A set for which both endpoints are real numbers.

Related Terms

Examples of bounded interval in the following topics:

  • Interval Notation

    • An interval is said to be bounded if both of its endpoints are real numbers.
    • Bounded intervals are also commonly known as finite intervals.
    • An interval that has only one real-number endpoint is said to be half-bounded, or more descriptively, left-bounded or right-bounded.
    • For example, the interval $(1, + \infty)$ is half-bounded; specifically, it is left-bounded.
    • Use interval notation to show how a set of numbers is bounded

  • 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.
    • If we know the confidence interval, we can work backwards to find both the error bound and the sample mean.
    • Subtract the error bound from the upper value of the confidence interval
    • Suppose we know that a confidence interval is (67.18, 68.82) and we want to find the error bound.
    • If we know the error bound: = 68.82 − 0.82 = 68

  • Changing the Confidence Level or Sample Size

    • 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.
    • What happens to the error bound and the confidence interval if we increase the sample size and use n=100 instead of n=36?
    • Increasing the sample size causes the error bound to decrease, making the confidence interval narrower.
    • Decreasing the sample size causes the error bound to increase, making the confidence interval wider.

  • Summary of Formulas

    • ( lower value,upper value ) = ( point estimate − error bound,point estimate + error bound )
    • Formula 8.2: To find the error bound when you know the confidence interval
    • error bound = upper value − point estimate OR error bound = (upper value − lower value)/2
    • The confidence interval has the format ($\bar{x}$ − EBM, $\bar{x}$ + EBM) .
    • The confidence interval has the format (p' − EBP, p' + EBP) .

  • Homework

    • Calculate the error bound.
    • Calculate the error bound.
    • Calculate the error bound.
    • What will happen to the error bound and confidence interval if 500 community colleges were surveyed?
    • What will happen to the error bound and confidence interval if 500 campers are surveyed?

  • Lab 2: Confidence Interval (Place of Birth)

    • The student will determine the effects that changing conditions have on the confidence interval.
    • Calculate the confidence interval and the error bound. i.
    • Error Bound:
    • Using the above information, construct a confidence interval for each given confidence level given.
    • Does the width of the confidence interval increase or decrease?

  • What Is a Confidence Interval?

    • A confidence interval is a type of interval estimate of a population parameter and is used to indicate the reliability of an estimate.
    • A confidence interval can be used to describe how reliable survey results are.
    • A confidence interval is a type of estimate (like a sample average or sample standard deviation), in the form of an interval of numbers, rather than only one number.
    • Confidence intervals correspond to a chosen rule for determining the confidence bounds; this rule is essentially determined before any data are obtained or before an experiment is done.
    • The confidence interval approach does not allow this, as in this formulation (and at this same stage) both the bounds of the interval and the true values are fixed values; no randomness is involved.

  • 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.
    • Error Bound:
    • Some students think that a 90% confidence interval contains 90% of the data.
    • Does the width of the confidence interval increase or decrease?

  • Introduction to Confidence Intervals

    • State why a confidence interval is not the probability the interval contains the parameter
    • These intervals are referred to as 95% and 99% confidence intervals respectively.
    • An example of a 95% confidence interval is shown below:
    • There is good reason to believe that the population mean lies between these two bounds of 72.85 and 107.15 since 95% of the time confidence intervals contain the true mean.
    • It is natural to interpret a 95% confidence interval as an interval with a 0.95 probability of containing the population mean.

  • Histograms

    • To create this table, the range of scores was broken into intervals, called class intervals.
    • There are three scores in the first interval, 10 in the second, etc.
    • Placing the limits of the class intervals midway between two numbers (e.g., 49.5) ensures that every score will fall in an interval rather than on the boundary between intervals.
    • The class frequency is then the number of observations that are greater than or equal to the lower bound, and strictly less than the upper bound.
    • Your choice of bin width determines the number of class intervals.