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

H_{0} :
= 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

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...

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(with line under) = 3.75 grams. Let x be a
random variable representing weights of hummingbirds in this part
of the Grand Canyon....

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...

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...

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 = 3.75 grams. Let x be a random variable
representing weights of hummingbirds in this part of the Grand
Canyon. We assume that...

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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 = 3.75 grams. Let x be a
random variable representing weights of hummingbirds in this part
of the Grand Canyon....

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 = 3.75 grams. Let x be a
random variable representing weights of hummingbirds in this part
of the Grand Canyon. We assume that x...

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 = 3.75 grams. Let x be a
random variable representing weights of hummingbirds in this part
of the Grand Canyon. We assume that x...

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