Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. + Suppose a small group of 18 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with o = 0.37 gram. (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (b) What conditions are necessary for your calculations? (c) Interpret your results in the context of this problem. (d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.15 for the mean weights of the hummingbirds. Step 1 (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? To find a confidence interval for the average weight of Allen's hummingbirds in the study region, you will need a point estimate for u, and you will either need to know the population standard deviation or estimate it. The point estimate for y is ji = x = . The distribution of the weights is assumed to be normal with a known population standard deviation of o =