Question 7 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
In early 2019, the US rate of recycling plastic water bottles was only 23%. A government agency designs an expensive program to increase the recycling rate. The program will be tested in Texas and, if successful, it will be used nationally. A hypothesis test is conducted with H0: The proportion of water bottles that are recycled is still 23% after the program, and Ha: The proportion of water bottles that are recycled is more than 23% after the program. What is a Type I error and its consequence in this context?
Answer
A
The agency concludes that the program increases the recycling rate, when in fact it does not. The program will not be implemented and will save the agency money.
B
The agency correctly concludes that the program increases the recycling rate. The program will be implemented and will increase water bottle recycling.
C
The agency concludes that the program increases the recycling rate, when in fact it does not. The program will be implemented at great cost without increasing the rate of water bottle recycling.
D
The agency concludes that the program does not increase the recycling rate, when in fact it does increase the rate. The agency will not implement the program, and the recycling rate will not improve.