Assume a random sample of size n is from a normal population. Assume a single sample t test is used to for hypothesis testing. The null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. If the sample size is decreased, and the Type I error rate is unchanged, then the Type II error rate will increase. A. True B. False

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Mathematics

Kiana Spence

7 October, 09:52

Assume a random sample of size n is from a normal population. Assume a single sample t test is used to for hypothesis testing. The null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. If the sample size is decreased, and the Type I error rate is unchanged, then the Type II error rate will increase. A. True B. False

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Brenda Mosley · Answer 1

True

Step-by-step explanation:

Type I and Type II are not independent of each other - as one increases, the other decreases.

However, increases in N cause both to decrease, since sampling error is reduced.

A small sample size might lead to frequent Type II errors, i. e. it could be that your (alternative) hypotheses are right, but because your sample is so small, you fail to reject the null even though you should.