Type I and Type II Errors AP Statistics

With an  $\alpha-level\$  of 5%, what is the power of a test against an alternative for which the probability of a Type II error is 3%?

• 3%

• 5%

• 95%

• 97%

• The power cannot be determined from the information given. 

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

What is the Power of a test?

• A strong force

• The probability that we correctly reject a false null hypothesis.

• The probability that we correctly accept a true null hypothesis.

• To reject the null, when the null is tree.

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

You plan to perform a hypothesis test with a level of significance of 0.05. What is the effect on the probability of committing a Type I error if the sample size is increased?

• The probability of committing a Type I error decreases

• The probability of committing a Type I error is unchanged

• The probability of committing a Type I error increases

• The effect cannot be determined without knowing the relevant standard deviation

• The effect cannot be determined without knowing if a Type II error is committed

An independent research firm conducted a study of 100 randomly selected children who were participating in a program advertised to improve mathematics skills. The results showed no statistically significant improvement in mathematics skills, using α = 0.05. The program sponsors complained that the study had insufficient statistical power. Assuming that the program is effective, which of the following would be an appropriate method for increasing power in this context.

• Use a two-sided test instead of a one-sided test.

• Use a one-sided test instead of a two-sided test.

• Use α = 0.01 instead of α = 0.05.

• Decrease the sample size to 50 children

• Increase the sample size to 200 children

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