Type I and Type II Errors Practice

Which of the following best describes a Type I error?

• The null is true, but we mistakenly reject it.
• The null is false and we reject it.
• The null is false, but we fail to reject it.
• The null is true but we fail to reject it.

Tags

CCSS.HSS.MD.B.7

Which of the following best describes a Type II error?

• The null is true but we mistakenly reject it.

• The null is false but we mistakenly reject it.

• The null is false but we fail to reject it.

• The null is true but we fail to reject it.

Tags

CCSS.HSS.MD.B.7

The probability of a type I error is

• alpha
• beta
• sigma
• 1-beta

Tags

CCSS.HSS.MD.B.7

One ESP (extra sensory perception) test asks the subject to view the backs of cards and identify whether a circle, square, star , or cross is on the front of each card. If p is the proportion of correct answers, this may be viewed as a hypothesis test with H₀: p = 0.25 and H_a: p > 0.25. The subject is recognized to have ESP when the null hypothesis is rejected. What would a Type II error result in?

• Correctly recognizing someone has ESP

• Mistakenly thinking someone has ESP

• Not recognizing that someone really has ESP

• Correctly realizing that someone doesn't have ESP

• Failing to understand the nature of ESP

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. What would the results be of Type I and Type II errors for the null hypothesis: The weather will remain dry?

• Type I error: don't cancel school but the snow storm hits.

  Type II error: the weather remains dry, but school is needlessly canceled.

• Type I error: the weather remains dry, but school is needlessly canceled.

  Type II error: don't cancel school, but the snow storm hits.

• Type I error: cancel school, and the storm hits.

  Type II error: don't cancel school , and the weather remains dry.

• Type I error: don't cancel school, and the snow storm hits.

  Type II error: don't cancel school , and the weather remains dry.

• Type I error: don't cancel school , and the weather remains dry.

  Type II error: cancel school, and the storm hits.

Tags

CCSS.HSS.MD.B.7

A researcher plans to conduct a test of hypotheses at the α = 0.01 significance level.  She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest.  The probability that the researcher will commit a Type I error is

• 0.01
• 0.10
• 0.90
• 0.99

When leaving for school, you make a judgement on these hypotheses. H_o: The weather will remain dry. H_a: It will rain. What are the results of the Type I and Type II errors?

• Type I: Needlessly carry around an umbrella all day. Type II: Get drenched

• Type I: Get drenched. Type II: Needlessly carry around an umbrella all day

• Type I: Carry umbrella & it rains. Type II: Carry no umbrella & it doesn't rain

• Type I: Get drenched. Type II: Carry umbrella & it rains

Tags

CCSS.HSS.MD.B.7

An environmental scientist wants to test the null hypothesis that an antipollution device for cars is not effective. Under which of the following conditions would a Type 1 error be committed?

• The scientist concludes that the antipollution device is effective when it actually is not.
• The scientist concludes that the antipollution device is not effective when it actually is. 
• The scientist concludes that the antipollution device is not effective when it actually is not. 
• A type 1 error cannot be committed in this situation. 

Tags

CCSS.HSS.IC.B.5

CCSS.HSS.MD.B.7

A hypothesis test was conducted concerning the proportion of drivers using high octane gasoline. The hypotheses are H₀: p=0.14 and H_a: p>0.14, and the p-value was 0.2588. What conclusion should you make?

• Reject H₀. There is strong evidence to suggest p > 0.14

• Reject H_a, There is not convincing evidence to suggest that p >0.14.

• Fail to reject H₀. There is not convincing evidence to suggest p > 0.14

• Accept H₀. There is not convincing evidence to suggest p >0.14

A hypothesis test was performed with hypotheses  $H_0:\ \mu=30$  vs.  $H_a:\ \mu>30$  .  Where  $\mu=$  the mean number of minutes spent on HW for all students.  A p-value of 0.0012 was obtained.  What conclusion do you make?

• The p-value is small, so fail to reject  $H_0$ .  We do not have convincing evidence that the mean amount of  time spend on HW is > 30. 

• The p-value is small, so fail to reject  $H_0$ .  We have convincing evidence that the mean amount of  time spend on HW is > 30. 

• The p-value is small, so reject  $H_0$ .  We do not have convincing evidence that the mean amount of  time spend on HW is > 30. 

• The p-value is small, so reject  $H_0$ .  We have convincing evidence that the mean amount of  time spend on HW is > 30.