1. A psychologist is studying learning in rats. They psychologist wants to determine the average time required for rats to learn to traverse a maze. She randomly selects 40 rats and records the time (in minutes) it takes them to traverse the maze. The sample average time is 5 minutes, with a sample standard deviation of 1 minute.

a. Use this information to compute a 95% confidence interval for the population mean time it takes rats to traverse the maze. Please clearly list the necessary conditions for inference, and show that you checked to make sure the data meet all necessary conditions for inference.

b. Interpret the meaning of the confidence interval you found in part a in the context of this application.

2. Acid rain accumulations in lakes and streams in the northeastern part of the United States are a major environmental concern. A researcher wants to know what fraction of lakes contain hazardous pollution levels. He randomly selects 200 lakes and determines that 45 of the selected lakes have an unsafe concentration of acid rain pollution.

a. Use this information to compute a 90% confidence interval for the population proportion of lakes with unsafe levels of acid rain pollution. Please clearly list the necessary conditions for inference, and show that you checked to make sure the data meet all necessary conditions for inference.

b. Interpret the meaning of the confidence interval you found in part a in the context of this application.