Question

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) 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 bar = 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 = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use α = 0.10.

(a) What is the level of significance? (Enter a number.)

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H0: μ < 4.3 g; H1: μ = 4.3 g; left-tailed

H0: μ = 4.3 g; H1: μ ≠ 4.3 g; two-tailed

H0: μ = 4.3 g; H1: μ < 4.3 g; left-tailed

H0: μ = 4.3 g; H1: μ > 4.3 g; right-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 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.

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

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

____

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

_____

Answer 1

Given:-

mu is population mean, sigma is population standard deviation, x(bar) is sample mean and n is sample size.

(A) Significance level is 0.10

Researcher want to test whether the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams. So, it is a left tailed hypothesis

Option C is correct

(B) Option A is correct because it has a standard normal distribution where population standard deviation is 0.64.

Therefore, option A is correct answer.

z statistics formula is

(C) Using excel function NORMSDIST(z)

using z = -2.11

we get

p value = NORMSDIST(-2.11)

= 0.0174

P value is less than 0.10 significance level, rejecting the null hypothesis as p value is significant. Enough evidence to support the statement that the mean is less than 4.3 grams