Reference no: EM132848037

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte annaxx). (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.3.72.93.84.24.83.1The sample mean is = 3.75 grams. Let be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that has a normal distribution and = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is = 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 = 0.10.(a) What is the level of significance? (Enter a number.)

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

1: H0: < 4.3 g; H1: = 4.3 g; left-tailed

2: H0: = 4.3 g; H1: < 4.3 g; left-tailed

3: H0: = 4.3 g; H1: ≠ 4.3 g; two-tailed

4: H0: = 4.3 g; H1: > 4.3 g; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

1: The standard normal, since we assume that x has a normal distribution with unknown.

2: The Student's t, since n is large with unknown.

3: The Student's t, since we assume that x has a normal distribution with known.

4: The standard normal, since we assume that x has a normal distribution with known.

Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)

(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.)