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11. [-10.22 Points] DETAILS BBUNDERSTAT12 8.1.021 . MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Bill Alther is a zoologist who studies Anna's hummingbird (Cauypte anna).t 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 lollows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is E = 3.75 grams. Letx be a random variable representing weights of hummingbirds in this part otthe Grand Canyon. We assume that x has a normal distribution and 0' = 0.72 gram. Suppose it is known that for the population of all Anna's hummingbirds. the mean weight is p. = 4.40 grams. Do the data indicate that the mean weight oi these birds in this part of the Grand Canyon is less than 4.40 grams? Use DC = 0.10. (a) What is the level of signicance? I: State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or twotailed test? 0 H0: p: 4.4 g; right-tailed O HO: u = 4.4 9; H1: p'. t 4.4 g;twoslailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 0 The Student's t. since I: is large with unknown 0'. O The Student's t. since we assume that x has a normal distribution with known on O The standard normal. since we assume that x has a normal distribution with known a: O The standard normal. since we assume that x has a normal distribution with unknown or. Compute the 2 value of the sample test statistic. (Round your answer to two decimal places.) I: (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) I: Sketch the sampling distribution and show the area corresponding to the Psvalue. 03 2 1 0 1 2 3 03 2 1 0 1 2 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signicant at level 0c? 0 At the or. = 0.1 0 level. we reject the null hypothesis and conclude the data are statistically signicant. 0 At the or, = 0.1 0 level. we reject the null hypothesis and conclude the data are not statistically signicant. 0 At the or. = 0.10 level. we fail to reject the null hypothesis and conclude the data are statistically signicant. 0 At the or. : 0.10 level. we fail to reject the null hypothesis and conclude the data are not statistically signicant. (e) State your conclusion in the context of the application. 0 There is sufcient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.40 grams. 0 There is insufcient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.40 grams