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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. 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?

*H*_{0}: *μ* = 4.3 g;
*H*_{1}: *μ* > 4.3 g; right-tailed

*H*_{0}: *μ* < 4.3 g;
*H*_{1}: *μ* = 4.3 g;
left-tailed

*H*_{0}: *μ* = 4.3 g;
*H*_{1}: *μ* ≠ 4.3 g; two-tailed

*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 unknown *σ*.

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

The Student's *t*, since we assume that *x* has a
normal distribution with known *σ*.

The Student's *t*, since *n* is large with unknown
*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

Solution : -

Giveh that

= 4.3

= 3.75

= 0.64

n = 6

a)

**What is the level of significance? (0.10)**

The null and alternative hypothesis is ,

H0 : = 4.3

Ha : < 4.3

This is the left tailed test .

**(b) The standard normal, since we assume that x
has a normal distribution with known σ.**

Test statistic = z

= ( - ) / / n

= (3.75 - 4.3 ) / 0.64 / 6

= -2.11

**The test statistic = -2.11**

P - value = P ( Z < -2.11 ) = 0.0174

**( c ) P-value = 0.0174**

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...

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...

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...

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).† 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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