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 = 0.92 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.60 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.60 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 = 4.6 g; H₁: μ > 4.6 g; right-tailed

_H₀: μ = 4.6 g; H₁: μ ≠ 4.6 g; two-tailed    

_H₀: μ = 4.6 g; H₁: μ < 4.6 g; left-tailed

_H₀: μ < 4.6 g; H₁: μ = 4.6 g; left-tailed

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

_The Student's t, since we assume that x has a normal distribution with known σ.

_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.

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


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

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

_At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

_At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.   

_At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

_At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.

_There is sufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.60 grams.

_There is insufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.60 grams.

Answer 1