Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) 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. 3.1 3.7 2.9 3.8 4.2 4.8 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 = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is µ = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use a = 0.10. %! (a) What is the level of significance? (Enter a number.) 10 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Họ: µ < 4.3 g; H1: µ = 4.3 g; left-tailed O Ho: H = 4.3 g; H: µ > 4.3 g; right-tailed O H: H = 4.3 g; H,: µ < 4.3 g; left-tailed O H: H = 4.3 g; H,: µ + 4.3 g; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown o. The Student's t, since we assume that x has a normal distribution with known o. O The Student's t, since n is large with unknown o. O The standard normal, since we assume that x has a normal distribution with known o. Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.) -2.19 (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.) 0072 Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.) 1:56 AM 1/9/2020