Question

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 σ = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.45 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.45 grams? Use α = 0.10.

(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?

H₀: μ = 4.45 g; H₁: μ ≠ 4.45 g; two-tailedH₀: μ < 4.45 g; H₁: μ = 4.45 g; left-tailed    H₀: μ = 4.45 g; H₁: μ > 4.45 g; right-tailedH₀: μ = 4.45 g; H₁: μ < 4.45 g; left-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 known σ.The Student's t, since n is large with unknown σ.    The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.

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

Answer 1