Question

4) A high school biology student wishes to test the hypothesis
that hummingbird feeders can affect the mean mass of ruby-throated
hummingbirds in the area surrounding the feeder. She captures and
weighs several of the hummingbirds near a science museum where
several feeders are located. She obtains the following masses in
grams: 4.4, 3.9, 4.5, 4.3, 4.1, 3.8, 3.8, 4.1, 3.9, 3.8, 3.2, 4.3
The student's hypotheses are: H0: µ= 3.65 g Ha: µ> 3.65 g Use
technology to calculate the P-value, then determine whether the
data provide sufficient evidence to conclude that the mean mass of
the birds in the area surrounding the feeder is greater than the
mean mass of the general population. Test at the 5% significance
level and assume that the population standard deviation is 0.35 g.
Also, assess the strength of the evidence against the null
hypothesis.

4)

A) P = 0.0002; since P <0.05, reject the null hypothesis. At the
5% significance level, the data do provide sufficient evidence to
conclude that the mean mass of the birds in the area surrounding
the feeder is greater than the mean mass of the general population.
The evidence against the null hypothesis is very strong.

B) P = 0.0004; since P <0.05, do not reject the null hypothesis. At the 5% significance level, the data do not provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is weak or none.

**How would i do this with the TI-84?**

Answer #1

H0: µ= 3.65

Ha: µ> 3.65

calculate sample mean for the given data using calculator we get

sample mean ( ) = 4.0083

population standard deviation ( ) = 0.35

sample size ( n ) = 12 , = 5% = 0.05

now use following steps by using TI-84 calculator

1) Press button STAT

2) then navigate to TESTS using RIGHT ARROW KEY

3) then press button 1 for Z test

4) now insert data as follows

5) now navigate to button CALCULATE and press ENTER

we get output as follows

here P-Value = 1.9541837E-4 = 0.00019 = 0.0002

P-Value = 0.0002

**A) P = 0.0002; since P <0.05, reject
the null hypothesis. At the 5% significance level, the data do
provide sufficient evidence to conclude that the mean mass of the
birds in the area surrounding the feeder is greater than the mean
mass of the general population. The evidence against the null
hypothesis is very strong.**

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...

1. In testing a null hypothesis H0 versus an alternative Ha, H0
is ALWAYS rejected if
A. at least one sample observation falls in the non-rejection
region.
B. the test statistic value is less than the critical value.
C. p-value ≥ α where α is the level of significance. 1
D. p-value < α where α is the level of significance.
2. In testing a null hypothesis H0 : µ = 0 vs H0 : µ > 0,
suppose Z...

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...

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 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...

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