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 = 0.94 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.65 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.65 grams? Use α = 0.10.

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

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 4.65

H_a : < 4.65

Test statistic = z

= ( - ) /    / n

= (3.75 - 4.65) / 0.94 / 6

Test statistic = -2.34  

P-value = 0.0095