Question 1165133: 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.
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.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! assuming all the randomness, normality, etc.
z=(x bar-mean)/s/sqrt(6)
=(3.75-4.30)*sqrt(6)/0.64
=-2.105 or -2.11
one way test p-value is 0.017
The data suggest that the mean weight of these birds is < 4.30 gm.
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