AP Statistics Type I and Type II Errors

Regulations from the EPA say that soil used in playgrounds should not have lead levels more than 400 ppm. Before beginning construction on a new site, a sample of soil is taken and tested. If the mean level of lead in this soil is significantly higher than 400 ppm, then construction cannot continue. Here are the hypotheses:

 $H_0:\ \mu\ =\ 400\ ppm$   $H_a:\ \mu\ >\ 400\ ppm$  

Which of the following would be a type I error?

• The soil is actually safe, the sample is below 400 ppm, so construction continues

• The soil is actually safe, and the sample is higher than 400 ppm, so construction stops

• The soil is actually unsafe, the sample is below 400 ppm, so construction continues

• The soil is actually unsafe, and the sample is higher than 400 ppm, so construction stops

Regulations from the EPA say that soil used in playgrounds should not have lead levels more than 400 ppm. Before beginning construction on a new site, a sample of soil is taken and tested. If the mean level of lead in this soil is significantly higher than 400 ppm, then construction cannot continue. Here are the hypotheses:

 $H_0:\ \mu\ =\ 400\ ppm$   $H_a:\ \mu\ >\ 400\ ppm$  

Which of the following would be a type II error?

• The soil is actually safe, the sample is below 400 ppm, so construction continues

• The soil is actually safe, and the sample is higher than 400 ppm, so construction stops

• The soil is actually unsafe, the sample is below 400 ppm, so construction continues

• The soil is actually unsafe, and the sample is higher than 400 ppm, so construction stops

A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this is true for her town, so she plans to take a sample of residents to see if the unemployment rate is significantly different than 9% in her town. Here are the hypotheses:

 $H_0:\ p\ =\ 0.09$   $H_a:\ p\ \ne0.09$  

Which of the following would be a type I error?

• She concludes the town's unemployment rate is not 9% when it actually is.

• She concludes the town's unemployment rate is not 9% when it actually is not.
  

• She concludes the town's unemployment rate is 9% when it actually is.
  

• She concludes the town's unemployment rate is 9% when it actually is not.
  

A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this is true for her town, so she plans to take a sample of residents to see if the unemployment rate is significantly different than 9% in her town. Here are the hypotheses:

 $H_0:\ p\ =\ 0.09$   $H_a:\ p\ \ne0.09$  

Which of the following would be a type II error?

• She concludes the town's unemployment rate is not 9% when it actually is.

• She concludes the town's unemployment rate is not 9% when it actually is not.
  

• She concludes the town's unemployment rate is 9% when it actually is.
  

• She concludes the town's unemployment rate is 9% when it actually is not.
  

A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested is higher than 40%, in which case they would consider building the new cafeteria. Here are the hypotheses they'll use:

 $H_0:\ p\ =\ 0.40$   $H_a:\ p\ >0.40$  

Which of the following would be the consequence of a Type I error?

• They don't consider building the new cafeteria when they should.

• They don't consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafteria when they should.
  

A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested is higher than 40%, in which case they would consider building the new cafeteria. Here are the hypotheses they'll use:

 $H_0:\ p\ =\ 0.40$   $H_a:\ p\ >0.40$  

Which of the following would be the consequence of a Type II error?

• They don't consider building the new cafeteria when they should.

• They don't consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafteria when they should.
  

A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested is higher than 40%, in which case they would consider building the new cafeteria. Here are the hypotheses they'll use:

 $H_0:\ p\ =\ 0.40$   $H_a:\ p\ >0.40$  

Which of the following would not be errors at all? (Select all that apply)

• They don't consider building the new cafeteria when they should.

• They don't consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafteria when they should.
  

How confident do you feel about identifying Type I and Type II errors?

• I feel very lost

• I sometimes understand

• I think I get it

• I feel very confident