Allen's hummingbird (Selasphorussasin) has been studied by zoologist Bill Alther.T Suppose a small group of 10 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 a = 0.38 gram. When finding an 80% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) 2. = x (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.) margin of error :] (b) What conditions are necessary for your calculations? (Select all that apply.) normal distribution of weights :1 is known n is large Cl uniform distribution of weights l: a is unknown (c) Interpret your results in the context of this problem. 0 We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval. 0 The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. (9 We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval. 0 The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. (d) Which equation is used to find the sample size n for estimating y when cr is known? , 'z 0' J n: V' i: or U Q n=(ZUU)2 E K I'zaE On: \\l (I Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.11 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) :l hummingbirds