Question

Increasing the significance level of a test increases the probability of a Type II error.

aTrue bFalse c Not sure

The larger the population variance, the higher the power of the test.

a True b False c Not sure

The larger the sample size, the greater the power of the test with everything else being equal.

a True b False c Not sure

Explain the relationship between Type I error and Type II error in a hypothesis test.

Answer 1

Increasing the significance level of a test increases the probability of a Type II error.

Aswer: b. False

Higher values of the level of significance, reduce the region of acceptance and makes it easier to reject the null hypothesis. So choosing higher level of significance can reduce the probability of a Type II error.

The larger the population variance, the higher the power of the test.

Aswer: b. False

The probability of making a type II error (failing to reject the null hypothesis when it is actually false) is called β (beta). The quantity (1 - β) is called Power .

Power of a test depends on variance. As the distributions become more variable within their own groups, there is less overlap between the H₀ and H_A groups. Hence, power decreases. Within-group variability decreases power, on the other hand, smaller variance increases power.

The larger the sample size, the greater the power of the test with everything else being equal.

Aswer: a. True

Power depends on sample size. Other things being equal, larger sample size yields higher power. As sample size increases, within-group variability (error variance) decreases. Thus, power increases.

Explain the relationship between Type I error and Type II error in a hypothesis test.

A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population. The probability of committing a type I error is called α (alpha) the other name for this is the level of statistical significance. The probability of making a type II error is called β (beta). The quantity (1 - β) is called power, the probability of observing an effect in the sample.

Type I and Type II errors are inversely related: As one increases, the other decreases.