Question

Ecology: Hummingbirds Bill Alther is a zoologist who studies Anna’s hummingbird (Calypte anna; Reference: Hummingbirds by K. Long and W. Alther). Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighted, and released. The weights (in grams) were 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 Anna’s hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.70 gram. 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 = 0.01.

Answer 1

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 4.55

H_a : < 4.55

Test statistic = z

= ( - ) /    / n

= (3.75 - 4.55) / 0.70 / 6

Test statistic = -2.80

P-value = 0.0026

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.55 grams