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. 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. (a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ = 4.3 g; H1: μ ≠ 4.3 g; two-tailed H0: μ = 4.3 g; H1: μ < 4.3 g; left-tailed H0: μ = 4.3 g; H1: μ > 4.3 g; right-tailed H0: μ < 4.3 g; H1: μ = 4.3 g; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with unknown σ. The Student's t, since we assume that x has a normal distribution with known σ. The standard normal, since we assume that x has a normal distribution with known σ. 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. (Enter a number. Round your answer to four decimal places.)

Answer #1

(a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

Answer :

level of significance = 0.10

The null and alternative hypothesis H_{0}: μ = 4.3 g;
H_{1}: μ < 4.3 g; left-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution with known

We will use Minitab to Compute the z value of the sample test statistic:

Test statistic value is -2.11

(c) Find (or estimate) the P-value is 0.0174

Hope this will be helpful. Thanks and God Bless You :)

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...

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...

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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....

1. 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...

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...

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).† 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...

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