Question

For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is

requals=0.715

Using

alphaαequals=0.05,

determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

a. Is there a linear correlation between chest size and weight?

A.Yes, because the test statistic falls between the critical values of

negative 0.707−0.707

and 0.707.

B.Yes, because the absolute value of the test statistic exceeds the critical value

of 0.707

C.No, because the absolute value of the test statistic exceeds the critical value

of 0.707

D.

The answer cannot be determined from the given information.

b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

nothing

Answer #1

Solution:

We are given

r = 0.715

α = 0.05

n = 8

df = n – 2 = 8 – 2 = 6

So, critical value by using correlation critical values table is given as below:

Critical value = 0.707

r > critical value, so we reject the null hypothesis

There is sufficient evidence to conclude that there is a linear correlation between chest size and weight.

a. Is there a linear correlation between chest size and weight?

**B.Yes, because the absolute value of the test statistic
exceeds the critical value of 0.707**

b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

We are given r = 0.715

Coefficient of determination = R^2 = r^2 = 0.715^2 = 0.511225 = 51.12%

About 51.12% of the proportion of the variation in weight can be explained by the linear relationship between weight and chest size.

**Answer:** **0.511225**

For a sample of eight bears, researchers measured the distances
around the bears' chests and weighed the bears. Minitab was used
to find that the value of the linear correlation coefficient is
r=0.992 Using alpha=0.05, determine if there is a linear
correlation between chest size and weight. What proportion of the
variation in weight can be explained by the linear relationship
between weight and chest size?
a. Is there a linear correlation between chest
size and weight?
A.
No, because...

For a sample of eight bears, researchers measured the distances
around the bears' chests and weighed the bears. Minitab was used
to find that the value of the linear correlation coefficient is
r=0.963. Using α=0.05, determine if there is a linear correlation
between chest size and weight. What proportion of the variation in
weight can be explained by the linear relationship between weight
and chest size? What is the test statistic? (round to three
decimals)

For a sample of eight bears, researchers measured the distances
around the bears' chests and weighed the bears. Minitab was used
to find that the value of the linear correlation coefficient is r
equals=0.762. Using alpha α equals=0.05, determine if there is a
linear correlation between chest size and weight. What proportion
of the variation in weight can be explained by the linear
relationship between weight and chest size?

Fifty dash four wild bears were anesthetized, and then their
weights and chest sizes were measured and listed in a data set.
Results are shown in the accompanying display. Is there sufficient
evidence to support the claim that there is a linear correlation
between the weights of bears and their chest sizes? When measuring
an anesthetized bear, is it easier to measure chest size than
weight? If so, does it appear that a measured chest size can be
used to...

Researchers initiated a? long-term study of the population of
American black bears. One aspect of the study was to develop a
model that could be used to predict a? bear's weight? (since it is
not practical to weigh bears in the? field). One variable thought
to be related to weight is the length of the bear. The accompanying
data represent the lengths and weights of 12 American black bears.
Complete parts? (a) through? (d) below.
Total Length (cm) Weight (kg)...

A scatter diagram is a graph that portrays a correlation between
a ________________variable and a _______________ variable.
The _________________ of _________________ is expressed as a
percent, its value is between 0 and 100%.
In plotting paired data in a scatter diagram, the independent
variable is scaled on the __________________.
If there is absolutely no relationship between two variables,
Pearson's r will equal _____.
________________________________________
If the coefficient of correlation is 0.80, the coefficient of
determination is _____.
________________________________________
The proportion...

A random sample of eight auto drivers insured with a
company and having similar auto insurance policies
was selected. The following table lists their driving experience
(in years) and the monthly auto insurance
premium (in dollars).
Driving Experience(years) 5 2 12 9 15 6 25 16
Monthly Premium(dollars) 64 87 50 71 44 56 42 60
Answer the following questions.
(a) Does the insurance premium depend on driving experience or does
the driving experience depend on
insurance premium? Do you...

To determine how climate change and habitat loss will influence
Antarctic species, baseline estimates of population sizes and
distributions are needed. To this end, a group of researchers
estimated the population sizes of all breeding colonies of emperor
penguins (Aptenodytes fosteri) along Antarctic coastlines
using satellite imagery (Fretwell et al., 2012). For each breeding
colony encountered, the researchers determined the latitude,
longitude, and area (m2) of the colony, and estimated
the total number of emperor penguins present. Then, they compared...

Q3) In a difference of proportion test with alpha= .01, the
critical value for a one tailed lower test is/are:
A) -1.96 B) -1.645 and 1.645
C) -2.33 D) -1.28
Q4) If the test statistic for a small sample difference of means
test is t*=-2.15, we could reject the Null Hypothesis at alpha =.01
for a two tailed test with degrees of freedom equal to 20:
true or false
Q9) In a difference of MEans test there are two sources...

PLEASE FILL IN THE BLANKS WITH THE PROPER TERM! THANKS
Key Terms
----------------------------------------------------------------------------------------------------------------------------
Positive relationship --- Occurs in so far as pairs of
observations tend to occupy similar relative positions in their
respective distribution.
Negative relationship --- Occurs in so far as pairs of
observations tend to occupy dissimilar relative positions in their
respective distribution.
Scatterplot --- a graph containing a cluster of dots
that represents all pairs of observations.
Person correlation coefficient --- A number between –1
and +1...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 9 minutes ago

asked 13 minutes ago

asked 16 minutes ago

asked 17 minutes ago

asked 37 minutes ago

asked 39 minutes ago

asked 40 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago