9.2 Outcomes and the Type I and Type II Errors

Rejecting a true null versus keeping a false one, the probabilities alpha and beta attached to each, and stating both mistakes in the problem's own terms.

Statistics, 9.2 Outcomes and the Type I and Type II Errors

Status

FlagsLoading your progress…

12 exercises

9.2 Exercise 1

Suppose the null hypothesis, H₀, is: the blood cultures contain no traces of pathogen X. State the Type I and Type II errors.

2.5

9.2 Exercise 2

Suppose the null hypothesis, H₀, is: a patient is not sick. Which type of error has the greater consequence, Type I or Type II?

2.5

9.2 Exercise 3

Red tide is a bloom of poison-producing algae—a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts, the Division of Marine Fisheries montors levels of the toxin in shellfish by regular sampling of shellfish…

2.5

9.2 Exercise 4

Assume a null hypothesis, H₀, that states the percentage of adults with jobs is at least 88 percent.

Identify the Type I and Type II errors from these four possible choices.

Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88 percent when that percentage is actually less than 88 percent
Not to reject the null hypothesis that the percentage of adul…

2.5

9.2 Exercise 5

The mean price of mid-sized cars in a region is $32,000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.

2.5

9.2 Exercise 7

For Exercise 9.12, what are α and β in words?

2.5

9.2 Exercise 9

A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H₀, is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.

2.5

9.2 Exercise 11

The power of a test is 0.981. What is the probability of a Type II error?

2.5

9.2 Exercise 13

A microbiologist is testing a water sample for E. coli. Suppose the null hypothesis, H₀, is the sample does not contain E. coli. The probability that the sample does not contain E. coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E. coli, but the microbiologist thinks it does not is 0.002. What is the power of this test?

2.5

9.2 Exercise 15

State the Type I and Type II errors in complete sentences given the following statements.

The mean number of years Americans work before retiring is 34.
At most 60 percent of Americans vote in presidential elections.
The mean starting salary for San Jose State University graduates is at least $100,000 per year.
29 percent of high school students take physical education every day.
Less than 5 perce…

2.5

9.2 Exercise 17

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the U.S. Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is the drug is unsafe. What is the Type II error?

To conclude the drug is safe when, in fact, it is unsafe.
Not to conclude the drug is safe when, in fact, it is safe.
To conclude…

2.5

9.2 Exercise 19

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5 percent, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on averag…

2.5