Type 1 and Type II Errors

Type 1 and Type II Errors

Follow Along with Page 5 - 6 In your notes

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

1.    State appropriate hypotheses for performing a significance test using words and symbols.​

Remember: Null is what is claimed to be true

Alternative is what we are trying to prove​

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

2.    After conducting a significance test, a P-value of 0.045 is found. Interpret this value.

This is in the form:

Assuming null is true there is a p-value probability of getting the sample statistics or "more extreme"​

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

3.  Based on the P-value, should Rockford keep the current water or switch to bottled water? Explain.

Hint: Is the water safe?​

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

4.  Let’s suppose this decision is wrong.  What would be a consequence of this error?​

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

5. Given the water is safe, how often will this error occur?

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

6.    Now suppose the P-value was 0.14.  Should the town keep the current water or switch to bottled water?​

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

7.    Let’s suppose this decision is wrong.  What would be a consequence of this error?

​The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS), which have leaked into the ground water. The state’s drinking water limit of 70 parts per trillion (ppt) is considered safe, while anything above 70 ppt is considered dangerous. Officials believes the water in Rockford may be unsafe. They take a random sample of 200 households in Rockford. They find the average lead level of the sample is 70.5 ppt.

8. Are the consequences in question #4 or question #7 more serious?  Explain.

Watch the 6.7 Video in AP Classroom on Type I and Type II Errors. Take notes in the important ideas box on page 4 in your notes. Fix any of your answers based on these notes.

​

Important Ideas

​https://apclassroom.collegeboard.org/d/6tvg0n0vow?sui=33,6

Work on Homework - Due Friday

9.1 Quiz - Friday​

Others - Interpreting the p-value, ​drawing accurate conclusions

#7 - State the mistake

State: Ho, Ha, and parameter of interest

#5 - Standard deviation can be our measurement​

#1 ,3 ,5