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 = 0.72 gram.
suppose it is known that for the population of all anna's hummingbirds, the mean weight is μ = 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 α = 0.10.

(a) what is the level of

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: μ = 4.55 g; h1: μ < 4.55 g; left-tailed

b. h0: μ < 4.55 g; h1: μ = 4.55 g; left-tailed

c. h0: μ = 4.55 g; h1: μ ≠ 4.55 g; two-tailed

d. h0: μ = 4.55 g; h1: μ > 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 σ.

b. the standard normal, since we assume that x has a normal distribution with unknown σ.

c. the student's t, since we assume that x has a normal distribution with known σ.

d. the standard normal, since we assume that x has a normal distribution with known σ.

what is the value of the sample test (round your answer to two decimal places.)

(c) find (or estimate) the p- (round your answer to four decimal places.)