Question 18 • 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 II 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 be implemented at great cost to the agency.
B
The agency concludes that the program does not increase the recycling rate, when in fact it does. The program will be implemented and will increase water bottle recycling.
C
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 a program that could have increased the water bottle recycling rate.
D
The agency concludes that the program increases the recycling rate, when in fact it does not. The agency will not implement a program that could have increased the water bottle recycling rate.
Explanation
A Type II error occurs when the null hypothesis is not rejected even though the alternative hypothesis is true. Here, that means concluding the program does not increase recycling above 23% when it actually does. The consequence is that the agency may not implement a program that could have increased the recycling rate, as choice C states.
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