Type 1 and Type 2 Errors Power

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.

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.

The probability of a type I error is

• alpha
• beta
• sigma
• 1-beta

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.

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

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

• 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. 

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%.

• 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.

Which of the following is true about Type I and Type II errors?

I. Type I errors are always worse than Type II errors.

II. The severity of Type I and Type II errors depend on the situation being tested

III. In any given situation, the higher the risk of Type I error, the lower the risk of Type II error.

• I only

• II only

• III only

• I and III

• II and III