Imagine that you are a researcher interested in examining the impact of taking daily walks on a person's level of happiness (sense of well-being). You decide to use a well-known scale of sense of well-being, which includes the average value people score (= 68) and the standard deviation (= 9).

1. (3 points) What is the probability that you would randomly select a sample ofn= 36 participants that had a mean within 3 points of the population mean? In other words,p(65 <M< 71)?
2. (2 points) You select a sample ofn= 36 participants and ask them to walk every day for at least 30 minutes. At the end of a month you give them the well-being scale and findM= 72. If you use a two-tailed test with= 0.05 to determine the impact of taking a daily walk on well-being, what is the probability that you have made a Type I error? How can you reduce the probability of making a Type I error?