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* = 0.66 gram. Suppose it is known that
for the population of all Anna's hummingbirds, the mean weight is
*μ* = 4.45 grams. Do the data indicate that the mean weight
of these birds in this part of the Grand Canyon is less than 4.45
grams? Use *α* = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a
left-tailed, right-tailed, or two-tailed test?

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

Compute the *z* value of the sample test statistic. (Round
your answer to two decimal places.)

(c) Find (or estimate) the *P*-value. (Round your answer to
four decimal places.)

Sketch the sampling distribution and show the area corresponding to
the *P*-value.

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level *α*?

(e) State your conclusion in the context of the application.

Answer #1

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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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