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# Type I and Type II Error

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It is claimed that a new treatment for prolonging the life of patients with leukemia is more effective than previous treatments. The null and research or alternative hypotheses for a data set are: Ho: mu < 10.6 years and Ha: mu > 10.6 years (claim).

a. State the research conclusion that was written if Ho was rejected and a Type I error was made.
b. State the research conclusion that was written if Ho was not rejected and a Type II error was made.
c. State the research conclusion that was written if a sample size of 15 with an alpha level of 0.05 has a test value of 2.27?

##### Solution Summary

It is claimed that a new treatment for prolonging the life of patients with leukemia is more effective than previous treatments. The null and research or alternative hypotheses for a data set are: Ho: mu < 10.6 years and Ha: mu > 10.6 years (claim).

a. State the research conclusion that was written if Ho was rejected and a Type I error was made.
b. State the research conclusion that was written if Ho was not rejected and a Type II error was made.
c. State the research conclusion that was written if a sample size of 15 with an alpha level of 0.05 has a test value of 2.27?

##### Solution Preview

First, a few words about Type I and II errors:
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<br><br>There are two kinds of errors that can be made in significance testing: (1) a true null hypothesis can be incorrectly rejected and (2) a false null hypothesis can fail to be rejected. The former error is called a Type I error and the latter error is called a Type II error.
<br><br>These two types of errors are defined in the attached table. The probability of a Type I error is designated by the Greek letter alpha (a) and is called the Type I error rate; the probability of a Type II error (the Type II error rate) is designated by the Greek letter beta (à?) .
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<br><br>A Type II error is only an error in the sense that an opportunity to reject the null hypothesis ...

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