Bill Alther is a zoologist who studies Annas hummingbird Cal

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 = 0.72 gram. Suppose it is known that for the population of all Anna\'s hummingbirds, the mean weight is = 4.55 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.55 grams? Use = 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? Select A, B, C, or D

A. H0: = 4.55 g; H1: < 4.55 g; left-tailed

B. H0: < 4.55 g; H1: = 4.55 g; left-tailed

C. H0: = 4.55 g; H1: 4.55 g; two-tailed

D. H0: = 4.55 g; H1: > 4.55 g; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Select A, B, C or D

A. The Student\'s t, since n is large with unknown .

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

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

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

What is the 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.)

Solution

(a) What is the level of significance?_____________ 0.10

H0: = 4.55 g; H1: < 4.55 g; left-tailed

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

Z = 3.75 - 4.55 / 0.72

Z = -1.11

p value : 0.1335