Practice with Type I/Type II Errors

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

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

Because of the expense of running a campaign, a potential candidate will only run if there is more than 40% initial support for him. To test this they take a SRS of 200 voters and ask if they would vote for him. They run a significance test with H₀: p = 0.40 vs. H_a: p > 0.40. Which of the following describes a consequence of Type II error in this setting?

• Thinking that there is enough support, but the candidate still decides not to run for office.

• Thinking that there is not enough support, but the candidate still decides to run for office.

• Thinking that there is not enough support, so the candidate decides not to run for office. The candidate saves money, but might have won because the initial support is more than 40%

• Thinking that there is enough support, so the candidate decides to run for office. This is a waste of money because the initial support is not more than 40%.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.4

CCSS.HSS.MD.B.7

A lightbulb company claims that their lightbulbs last 1000 hours. To test this claim, a consumer selects a random sample of 20 lightbulbs manufactured by the company. The consumer turned on the lightbulbs and recorded the time it took until the lightbulbs burned out. A significance test is performed using the following hypotheses at the 5% significance level:  $H_0:\ \mu\ =1000\ vs.\ H_a:\ \mu\ <1000$ where  $\mu$  =the mean time until burn out for all lightbulbs from this company.  Which of the following describes a Type I error in this setting?  

• The consumer does not find convincing evidence that the lightbulbs last, on average, 1000 hours, when it fact the P-value of the test was not small enough to reject the null hypothesis.

• The consumer does not find convincing evidence that the lightbulbs last, on average, 1000 hours, when it fact the P-value of the test was small enough to reject the null hypothesis.

• The consumer finds convincing evidence that the lightbulbs last, on average, 1000 hours, when it fact the lightbulbs last less than 1000 hours, on average.

• The consumer advocate finds convincing evidence that the lightbulbs last, on average, less than 1000 hours, when it fact the lightbulbs last 1000 hours, on average.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.5