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. 37|25 3842|4831 The somple 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 = 0.62 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is x = 4.40 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.40 grams? Use @ = 0.01, (a) What is the level of significance? State the null and alternate hypotheses (in grams). (Enter 1= for # as needed.) you use a left-tailed, right-tailed, or two-tailed test? ) right-tailed ) left-tailed O two-tailed o (b) What sam| ing distribution will you use? Explain the rationale for your choice of sampling distribution. 2 We'll use the standard normal, since we assume that x has a normal distribution with unknown . ) we'll use the Student's , since we assume that x has a normal distribution with known &. ) We'll use the standard normal, since we assume that x has a normal distribution with known 7. we'll use the Student's , since n is large with unknown o. Compute the 2 value of the sample test statistic. (Round your answer to two decimal places.) (