Which of the following regarding the Type I and Type II errors of a significance

Question

Which of the following regarding the Type I and Type II errors of a significance test is/are correct? Select all that apply. The power of test1 P(Type II error) For a fixed significance level a, the probability of a Type II error increases when the sample size increases P(Type II error) -1 - P(Type I error) The probability of a Type II error would decrease if the true population parameter value is further away from the presumed parameter value stated in the null hypothesis For a fixed sample size n, the probability of a Type II error increases when the probability of a Type I error decreases. For a fixed significance level , the probability of a Type I error increase when the sample size increases

Explanation / Answer

Ans:

First ,fourth and fifth statements are correct.

1)Power=1-type II error (correct)

2)For a fixed alpha,the probability of type II error increases,when sample size increases(incorrect)

Type II error should decrease when sample size,n is increased,as test statistic increases with increasing n,and we will be more likely to reject null hypothesis.

3)Type II error=1-Type I errror (Incorrect)

4)The probability of type II error would decrease,if the true population parameter value is further away from the persumed parameter value stated in the null hypothesis.(as test statistic value will increase and we will be more likely to reject null hypothesis) (correct)

5)For a fixed sample size,the probability of type II error increaases when the probability of a Type I error decreases.(correct)

6)For a fixed significance alpha ,the probability of a type I error increase when sample size increases.(Incorrect)

P(type I error)=alpha,so it is fixed,when n increases,we are more likely to reject null hypothesis,type II error reduces,hence it increase the power of the test,but Probabilty of type I error is fixed.

Ref:

Type I error

When the null hypothesis is true and you reject it, you make a type I error. The probability of making a type I error is , which is the level of significance you set for your hypothesis test. An of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis. To lower this risk, you must use a lower value for . However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists.

Type II error

When the null hypothesis is false and you fail to reject it, you make a type II error. The probability of making a type II error is , which depends on the power of the test. You can decrease your risk of committing a type II error by ensuring your test has enough power. You can do this by ensuring your sample size is large enough to detect a practical difference when one truly exists.

The probability of rejecting the null hypothesis when it is false is equal to 1–. This value is the power of the test.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.