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 = 0.82 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; left-tailed

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

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ. 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 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.)_____________

Answer 1

a. The level of significance is defined as the probability of rejecting a null hypothesis by the test when it is really true, which is denoted as α. That is, P (Type I error) = α. Confidence level: ... The level of significance 0.10 is related to the 90% confidence

level.

H0: μ = 4.6 g; H1: μ < 4.6 g; left-tailed

b) I will use stratigraphic random sampling distribution, first, identify which one is the best part and which one is a bad part then random sampling within the bad part and within the best part. but first necessary to know area cover by birds then select at least 20-30 birds weight in a given area

z = ( sampling mean - population mean)/standard error

= (3.75-4.60)/0.82

= -1.036585

c) p-value = 0.150101.