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 = 0.68 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.40 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.40 grams? Use α = 0.10.

Answer 1

in a normal distribution z = (