type II error

(noun)

Accepting the null hypothesis when the null hypothesis is false.

Related Terms

Examples of type II error in the following topics:

  • Outcomes and the Type I and the Type II Errors

    • The decision is to not reject Ho when, in fact, Hois false (incorrect decision known as a Type II error).
    • β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.
    • The following are examples of Type I and Type II errors.
    • Type II error: Frank thinks that his rock climbing equipment may be safe when, in fact, it is not safe.
    • Notice that, in this case, the error with the greater consequence is the Type II error.

  • Type I and Type II Errors

    • The two types of error are distinguished as type I error and type II error.
    • What we actually call type I or type II error depends directly on the null hypothesis, and negation of the null hypothesis causes type I and type II errors to switch roles.
    • A type II error occurs when the null hypothesis is false but erroneously fails to be rejected.
    • A type II error is committed when we fail to believe a truth.
    • Distinguish between Type I and Type II error and discuss the consequences of each.

  • Type I and II Errors

    • This type of error is called a Type I error.
    • This kind of error is called a Type II error.
    • Unlike a Type I error, a Type II error is not really an error.
    • A Type II error can only occur if the null hypothesis is false.
    • If the null hypothesis is false, then the probability of a Type II error is called β (beta).

  • Summary of Formulas

    • α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.
    • β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

  • Student Learning Outcomes

  • Solution to Exercises in Chapter 10

    • Type I error: We conclude that the mean is not 34 years, when it really is 34 years.
    • Type II error: We do not conclude that the mean is not 34 years, when it is not really 34 years.
    • Type II error: We do not conclude that the mean is less than $100,000, when it is really less than $100,000.
    • Type II error: We do not conclude that the proportion of h.s. seniors that get drunk each month is not 29%, when it is really not 29%.
    • Type II error: We do not conclude that the proportion is less than 11%, when it really is less than 11%.

  • Sample size and power exercises

    • (a) The standard error of ¯ x when s = 120 and (I) n = 25 or (II) n = 125.
    • (b) The margin of error of a confidence interval when the confidence level is (I) 90% or (II) 80%.
    • (d) The probability of making a Type 2 error when the alternative hypothesis is true and the significance level is (I) 0.05 or (II) 0.10.
    • (b) Decreasing the significance level (α) will increase the probability of making a Type 1 error.
    • If the null hypothesis is harder to reject (lower α), then we are more likely to make a Type 2 error.

  • Bias

    • While conducting measurements in experiments, there are generally two different types of errors: random (or chance) errors and systematic (or biased) errors.
    • All measurements are prone to systematic errors, often of several different types.
    • This type of error can be greatly reduced if you are familiar with the experiment you are doing.
    • Calibration can eliminate this type of error.
    • Method Errors: This type of error many times results when you do not consider how to control an experiment.

  • Chance Error

    • Random, or chance, errors are errors that are a combination of results both higher and lower than the desired measurement.
    • While conducting measurements in experiments, there are generally two different types of errors: random (or chance) errors and systematic (or biased) errors.
    • A random error makes the measured value both smaller and larger than the true value; they are errors of precision.
    • In this case, there is more systematic error than random error.
    • In this case, there is more random error than systematic error.

  • Impact of Measurement Error

    • Measurement error leads to systematic errors in replenishment and inaccurate financial statements.
    • Measurement error is the difference between the true value of a quantity and the value obtained by measurement.
    • The two main types of error are random errors and systematic errors.
    • In sum, systematic measurement error can lead to errors in replenishment.
    • As a result, an incorrect inventory balance causes an error in the calculation of cost of goods sold and, therefore, an error in the calculation of gross profit and net income.