Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). + Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean Is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and o = 0.98 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is A = 4.70 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.70 grams? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Hoi H = 4.7 9; Hi: p # 4.7 9; two-talled O Hoill = 4.7 9; H,: H 4.7 9; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with unknown o. The standard normal, since we assume that x has a normal distribution with known a. The Student's t, since n is large with unknown o. The Student's t, since we assume that x has a normal distribution with known a. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value