By Consumer Dummies

When you are doing hypothesis testing, you must be clear on Type I and Type II errors in the real sense — as false alarms and missed opportunities. Solve the following problems about Type I and Type II errors.

Sample questions

  1. Which of the following describes a Type I error?

    A. accepting the null hypothesis when it is true

    B. failing to accept the alternative hypothesis when it is true

    C. rejecting the null hypothesis when it is true

    D. failing to reject the alternative hypothesis when it is false

    E. none of the above

    Answer: C. rejecting the null hypothesis when it is true

    You make a Type I error when the null hypothesis is true but you reject it. This error is just by random chance, because if you knew for a fact that the null was true, you certainly wouldn’t reject it. But there’s a slim chance (alpha level) that it could happen.

    A Type I error is sometimes referred to as a “false alarm,” because rejecting the null hypothesis is like sounding an alarm to change an established value. If the null is true, then there’s no need for such a change.

  2. Which of the following describes a Type II error?

    A. accepting the alternative hypothesis when it is true

    B. failing to accept the alternative hypothesis when it is true

    C. rejecting the null hypothesis when it is true

    D. failing to reject the null hypothesis when it is false

    E. none of the above

    Answer: D. failing to reject the null hypothesis when it is false

    You make a Type II error when the null hypothesis is false but you fail to reject it because your data couldn’t detect it, just by chance.

    This error is sometimes referred to as “missing out on a detection.” The claim really was wrong, but you didn’t get a random sample that would provide enough evidence to reject it with enough statistical significance (small enough p-value).

  3. If the alpha level is 0.01, what is the probability of a Type I error?

    Answer: 0.01

    The alpha level (or significance level) of 0.01 indicates the probability of a Type I error — that is, the error of rejecting the null hypothesis when it’s actually true.

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