Question

A random sample of *n*_{1} = 10 regions in New
England gave the following violent crime rates (per million
population).

*x*_{1}: New England Crime
Rate

3.5 | 3.9 | 4.0 | 4.1 | 3.3 | 4.1 | 1.8 | 4.8 | 2.9 | 3.1 |

Another random sample of *n*_{2} = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).

*x*_{2}: Rocky Mountain Crime
Rate

3.9 | 4.3 | 4.7 | 5.3 | 3.3 | 4.8 | 3.5 | 2.4 | 3.1 | 3.5 | 5.2 | 2.8 |

Assume that the crime rate distribution is approximately normal in both regions.

(i) Use a calculator to calculate *x*_{1},
*s*_{1}, *x*_{2}, and
*s*_{2}. (Round your answers to three decimal
places.)

x_{1} |
= |

s_{1} |
= |

x_{2} |
= |

s_{2} |
= |

(ii) Do the data indicate that the violent crime rate in the Rocky
Mountain region is higher than in New England? Use *α* =
0.01.

(A) What is the level of significance?

_______________

State the null and alternate hypotheses.

*a) H*_{0}: *μ*_{1} =
*μ*_{2}; *H*_{1}:
*μ*_{1} > *μ*_{2}

*b) H*_{0}: *μ*_{1} <
*μ*_{2}; *H*_{1}:
*μ*_{1} =
*μ*_{2}

*c) H*_{0}: *μ*_{1} =
*μ*_{2}; *H*_{1}:
*μ*_{1} < *μ*_{2}

*d) H*_{0}: *μ*_{1} =
*μ*_{2}; *H*_{1}:
*μ*_{1} ≠ *μ*_{2}

(B) What sampling distribution will you use? What assumptions are
you making?

a) The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

b) The Student's *t*. We assume that both population
distributions are approximately normal with unknown standard
deviations.

c) The Student's *t*. We assume that both population
distributions are approximately normal with known standard
deviations.

d) The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the
difference *μ*_{1} − *μ*_{2}. Round
your answer to three decimal places.)

_______________

(C) Find (or estimate) the *P*-value.

*a) P*-value > 0.250

b) 0.125 < *P*-value <
0.250 0.050 < *P*-value <
0.125

c) 0.025 < *P*-value < 0.050

d) 0.005 < *P*-value < 0.025

*e) P*-value < 0.005

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*?

a) At the *α* = 0.01 level, we fail to reject the null
hypothesis and conclude the data are statistically significant.

b) At the *α* = 0.01 level, we fail to reject the null
hypothesis and conclude the data are not statistically
significant.

c) At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant.

d) At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are not statistically significant.

(E) Interpret your conclusion in the context of the
application.

a) Fail to reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.

b) Fail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.

c) Reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.

d) Reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.

Answer #1

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New England Crime
Rate
3.5
3.7
4.2
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky Mountain Crime
Rate
3.9
4.1
4.5
5.1
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution...

A random sample of n1 = 10 regions in New England gave the
following violent crime rates (per million population).
x1: New England Crime Rate 3.3 3.9 4.2 4.1 3.3 4.1 1.8 4.8 2.9
3.1
Another random sample of n2 = 12 regions in the Rocky Mountain
states gave the following violent crime rates (per million
population).
x2: Rocky Mountain Crime Rate 3.5 4.3 4.5 5.3 3.3 4.8 3.5 2.4
3.1 3.5 5.2 2.8
Assume that the crime rate distribution...

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New
England Crime Rate
3.3
3.7
4.2
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky
Mountain Crime Rate
3.9
4.1
4.5
5.5
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution is approximately...

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New
England Crime Rate
3.3
3.7
4.2
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky
Mountain Crime Rate
3.5
4.3
4.5
5.5
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution is approximately...

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New England Crime
Rate
3.5
3.9
4.0
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky Mountain Crime
Rate
3.7
4.1
4.7
5.3
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution...

A random sample of
n1 = 49
measurements from a population with population standard
deviation
σ1 = 3
had a sample mean of
x1 = 13.
An independent random sample of
n2 = 64
measurements from a second population with population standard
deviation
σ2 = 4
had a sample mean of
x2 = 15.
Test the claim that the population means are different. Use
level of significance 0.01.
(a) Check Requirements: What distribution does the sample test
statistic follow? Explain....

A random sample of
n1 = 49
measurements from a population with population standard
deviation
σ1 = 5
had a sample mean of
x1 = 8.
An independent random sample of
n2 = 64
measurements from a second population with population standard
deviation
σ2 = 6
had a sample mean of
x2 = 11.
Test the claim that the population means are different. Use
level of significance 0.01.(a) Check Requirements: What
distribution does the sample test statistic follow? Explain.
The...

The Wind Mountain archaeological site is in southwest New
Mexico. Prehistoric Native Americans called Anasazi once lived and
hunted small game in this region. A stemmed projectile point is an
arrowhead that has a notch on each side of the base. Both stemmed
and stemless projectile points were found at the Wind Mountain
site. A random sample of n1 = 55 stemmed projectile points showed
the mean length to be x1 = 3.00 cm, with sample standard deviation
s1 =...

A study of fox rabies in a country gave the following
information about different regions and the occurrence of rabies in
each region. A random sample of
n1 = 16
locations in region I gave the following information about the
number of cases of fox rabies near that location.
x1:
Region I Data
1
8
8
8
6
8
8
1
3
3
3
2
5
1
4
6
A second random sample of
n2 = 15
locations in...

The Wind Mountain archaeological site is in southwest New
Mexico. Prehistoric Native Americans called Anasazi once lived and
hunted small game in this region. A stemmed projectile point is an
arrowhead that has a notch on each side of the base. Both stemmed
and stemless projectile points were found at the Wind Mountain
site. A random sample of n1 = 60 stemmed
projectile points showed the mean length to be
x1 = 3.00 cm, with sample standard deviation
s1 =...

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