Type I and II Errors/Tests

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

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures
• Pythagorean Theorem
• t procedures
• np > 10 and n(1-p) > 10

The null hypothesis always contains a(an):

• < or >
• =
• >
• = or >

When p-value is greater than alpha we:

• Accept Ho
• Accept Ha
• Fail to reject Ho
• Reject Ho

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.
• The probability that we correctly accept a true null.
• How tough it is.

What does it mean when a test is statistically significant?

• it has reached alpha level status
• the test statistic had a P-value higher than the alpha level
• the test statistic had a P-value lower than the alpha level
• it is important in practical terms

How do you reduce both types of errors from occurring?

• it can't be reduced
• redo the tests
• increase the sample size
• tamper with the data

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers do not believe this is so. They take a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. What set of hypotheses are they interested in testing?

• a) H0: m = 50,000 vs. Ha: m < 50,000

• b)H0: x̅ = 50,000 vs. Ha: x̅ < 50,000

• c)H0: m = 50,000 vs. Ha: m ≠ 50,000

• d)H0: m = 50,000 vs. Ha: m > 50,000

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7 years with a standard deviation of 2 years. Do the data provide convincing evidence that the mean time of employment for the population of postal workers has changed from the value of 7.5 that was true 20 years ago? What conclusion should you draw at the 5% significance level?

• There is convincing evidence that the mean time working with the postal service has changed

• There is not convincing evidence that the mean time working with the postal service has changed

• There is convincing evidence that the mean time working with the postal service is still 7.5 years

• There is convincing evidence that the mean time working with the postal service is now 7 years

• We cannot draw a conclusion at the 5% significance level. The sample size is too small