Question

Bighorn sheep are beautiful wild animals found throughout the
western United States. Let *x* be the age of a bighorn sheep
(in years), and let *y* be the mortality rate (percent that
die) for this age group. For example, *x* = 1, *y* =
14 means that 14% of the bighorn sheep between 1 and 2 years old
died. A random sample of Arizona bighorn sheep gave the following
information:

x |
1 | 2 | 3 | 4 | 5 |

y |
13.0 | 20.5 | 14.4 | 19.6 | 20.0 |

Σ*x* = 15; Σ*y* = 87.5; Σ*x*^{2} =
55; Σ*y*^{2} = 1580.77; Σ*xy* = 275.6

Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.

(e) Given the result from part (c), is it practical to find
estimates of *y* for a given *x* value based on the
least-squares line model? Explain.

Given the significance of *r*, prediction from the
least-squares model is practical.Given the lack of significance of
*r*, prediction from the least-squares model might be
misleading. Given the lack of significance
of *r*, prediction from the least-squares model is
practical.Given the significance of *r*, prediction from the
least-squares model might be misleading

Answer #1

To Test :-

H0 :- ρ = 0

H1 :- ρ > 0

Test Statistic :-

t = (r * √(n - 2) / (√(1 - r2))

t = ( 0.5887 * √(5 - 2) ) / (√(1 - 0.3465) )

t = 1.2613

Test Criteria :-

Reject null hypothesis if t > t(α)

t(α,n-2) = t(0.05 , 5 - 2 ) = 2.3534

t < t(α, n-2) = 1.2613 < 2.3534

**Result :- We Accept H1**

Decision based on P value

P - value = P ( t > 1.2613 ) = 0.1482

Reject null hypothesis if P value < α = 0.05 level of
significance

P - value = 0.1482 > 0.05 ,**hence we fail to reject null
hypothesis**

**Conclusion :- We Accept H1**

Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.

Part e)

Given the lack of significance of *r*, prediction from
the least-squares model might be misleading.

Bighorn sheep are beautiful wild animals found throughout the
western United States. Let x be the age of a bighorn sheep
(in years), and let y be the mortality rate (percent that
die) for this age group. For example, x = 1, y =
14 means that 14% of the bighorn sheep between 1 and 2 years old
died. A random sample of Arizona bighorn sheep gave the following
information:
x
1
2
3
4
5
y
16.0
18.7
14.4...

Bighorn sheep are beautiful wild animals found throughout the
western United States. Let x be the age of a bighorn sheep
(in years), and let y be the mortality rate (percent that
die) for this age group. For example, x = 1, y =
14 means that 14% of the bighorn sheep between 1 and 2 years old
died. A random sample of Arizona bighorn sheep gave the following
information:
x
1
2
3
4
5
y
15.6
18.7
14.4...

Bighorn sheep are beautiful wild animals found throughout the
western United States. Let x be the age of a bighorn sheep
(in years), and let y be the mortality rate (percent that
die) for this age group. For example, x = 1, y =
14 means that 14% of the bighorn sheep between 1 and 2 years old
died. A random sample of Arizona bighorn sheep gave the following
information:
x
1
2
3
4
5
y
15.6
17.7
14.4...

11.4 #7
Let x be a random variable that represents the batting
average of a professional baseball player. Let y be a
random variable that represents the percentage of strikeouts of a
professional baseball player. A random sample of n = 6
professional baseball players gave the following information.
x
0.328
0.270
0.340
0.248
0.367
0.269
y
3.2
7.8
4.0
8.6
3.1
11.1
(a) Find ?x, ?y, ?x2,
?y2, ?xy, and r. (Round
r to three decimal places.)
?x =...

Wild irises are beautiful flowers found throughout the United
States, Canada, and northern Europe. This problem concerns the
length of the sepal (leaf-like part covering the flower) of
different species of wild iris. Data are based on information taken
from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part
2, pp. 179 -188). Measurements of sepal length in centimeters from
random samples of Iris setosa (I), Iris versicolor (II), and Iris
virginica (III) are as follows...

The correlation coefficient r is a sample statistic.
What does it tell us about the value of the population correlation
coefficient ρ (Greek letter rho)? You do not know how to
build the formal structure of hypothesis tests of ρ yet.
However, there is a quick way to determine if the sample evidence
based on ρ is strong enough to conclude that there is some
population correlation between the variables. In other words, we
can use the value of r...

The correlation coefficient r is a sample statistic.
What does it tell us about the value of the population correlation
coefficient ρ (Greek letter rho)? You do not know how to
build the formal structure of hypothesis tests of ρ yet.
However, there is a quick way to determine if the sample evidence
based on ρ is strong enough to conclude that there is some
population correlation between the variables. In other words, we
can use the value of r...

Ocean currents are important in studies of climate change, as
well as ecology studies of dispersal of plankton. Drift bottles are
used to study ocean currents in the Pacific near Hawaii, the
Solomon Islands, New Guinea, and other islands. Let x represent the
number of days to recovery of a drift bottle after release and y
represent the distance from point of release to point of recovery
in km/100. The following data are representative of one study using
drift bottles...

9.)What is the optimal time for a scuba diver to be on the
bottom of the ocean? That depends on the depth of the dive. The
U.S. Navy has done a lot of research on this topic. The Navy
defines the "optimal time" to be the time at each depth for the
best balance between length of work period and decompression time
after surfacing. Let x = depth of dive in meters, and let
y = optimal time in hours....

A sociologist is interested in the relation between x =
number of job changes and y = annual salary (in thousands
of dollars) for people living in the Nashville area. A random
sample of 10 people employed in Nashville provided the following
information.
x
(number of job changes)
4
3
5
6
1
5
9
10
10
3
y
(Salary in $1000)
38
34
31
32
32
38
43
37
40
33
In this setting we have ?x = 56,...

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