|
Interval Type
|
Confidence Level
|
n
|
α
|
z or t
|
z or t value
|
A
|
Two Tailed
|
90
|
45
|
.1
|
Z
|
1.64
|
B
|
Two Tailed
|
95
|
12
|
.05
|
T
|
2.201
|
C
|
One Tailed
|
95
|
36
|
.05
|
Z
|
1.64
|
D
|
Two Tailed
|
99
|
180
|
.01
|
Z
|
2.55
|
E
|
One Tailed
|
80
|
60
|
.2
|
Z
|
.845
|
F
|
One Tailed
|
99
|
23
|
.01
|
T
|
2.508
|
G
|
Two Tailed
|
99
|
15
|
.01
|
T
|
2.624
|
1.
A Department of the interior in Washington D.C.
estimates that the number of particular invasive species in a certain county
(Bucks County) should number as follows (averages based on data from the whole
state of Pennsylvania) per acre: Asian-Long Horned Beetle, 4; Emerald Ash Borer
Beetle, 10; and Golden Nematode, 75. A
survey of 50 fields had the following results: (10 pts)
μ σ
Asian-Long
Horned Beetle 3.2 0.73
Emerald Ash
Borer Beetle 11.7 1.3
Golden
Nematode 77 5.71
a.
Test the hypothesis for each of these
products. Assume that each are 2 tailed
with a Confidence Level of 95% *Use the appropriate test
a.
Asian-Long Horned Beetle
i. Null hypothesis: There is no significant
difference between the Asian-Long Horned beetle population of bucks county and
the mean of Pennsylvania
ii. Alternative Hypothesis: There is a significant
difference between the Asian-Long Horned beetle population of bucks county and
the mean of Pennsylvania
iii. Z-test statistic = -7.74911541
iv. Critical value = 1.96 or -1.96
v. -7.74911541 is less than -1.96, so the null
hypothesis is REJECTED!
b.
Emerald Ash Borer Beetle
i. Null hypothesis: There is no significant
difference between the long horned beetle population of bucks county and the
mean of Pennsylvania
ii. Alternative Hypothesis: There is a significant
difference between the long horned beetle population of bucks county and the
mean of Pennsylvania
iii. Z-test statistic = 9.25
iv. Critical value = 1.96 or -1.96
v. 9.25 is greater than 1.96, so the null
hypothesis is REJECTED!
c.
Golden Nemotode
i. Null hypothesis: There is no significant
difference between the golden nemotode population of bucks county and the mean
of Pennsylvania
ii. Alternative Hypothesis: There is a significant
difference between the golden nemotode population of bucks county and the mean
of Pennsylvania
iii. Z-test statistic = 2.47
iv. Critical value = 1.96 or -1.96
v. 2.47 is greater than 1.96, so the null
hypothesis is REJECTED!
b.
Be sure to present the null and alternative
hypotheses for each as well as conclusions
c.
What can ascertained pertaining to the findings
about these invasive species in Buck County?
a.
The populations of invasive species in Buck
County vary greatly from those in the rest of Pennsylvania.
2.
An exhaustive survey of all users of a
wilderness park taken in 1960 revealed that the average number of persons per
party was 2.1. In a random sample of 25
parties in 1985, the average was 3.4 persons with a standard deviation of 1.32
(one tailed test, 95% Con. Level) (5 pts)
a.
Test the hypothesis that the number of people
per party has changed in the intervening years.
(State null and alternative hypotheses)
a.
Null Hypothesis: The number of people per party
has not changed
b.
Alternative Hypothesis: The number of persons
per party has increased
c.
T-value = 4.924
d.
Probability value = 1.711
e.
4.924 is greater than 1.711, so the null is
rejected
b.
What is the corresponding probability value
Part II: Chi-Squared Testing
Introduction:
The tourism board of
Wisconsin wishes to determine what defines the concept of "Up-North",
as it relates to the state. In order to analyze this concept, three different
variables will be analyzed, to see if their distribution varies differently in
the northern versus southern regions of the state. The number of licenses sold
for the deer gun season will be analyzed, as it is a stereotypical feature of
the north. The percentage of the total population that purchased tags for gun
deer season will also be analyzed, as well as forest acreages.
Methods:
First, county shape file data was acquired from the
U.S. Census website, and an attribute value of 1 or 2 was given to the
counties depending on whether or not they were north or south of Highway 29 (Map 1).
Next, data from the Wisconsin Department of natural resources statewide
comprehensive outdoor recreation plan was joined to the shape files to
determine potential variables. After the variables I've been chosen, new fields
are added to the attribute table, and small integer values - between 1 and
4 - are assigned to them based on where they fall on an equidistant
classification. After all of the data sets have been classified, the data was
exported to SPSS for chi-squared calculations.
 |
| Map 1 |
Results:
The first Chi-squared test (Table 1) was to determine whether
or not the distribution of forest acreage was balanced between the northern and
southern parts of Wisconsin. For the tree acreage, the null hypothesis was that
there was no difference in the distribution of forest acreage between the
northern and southern parts of the state. The alternate I pop assist was that
the distribution of forest acreage was not even between the northern and
southern parts of the state. After calculating the chi-square test, the test
statistic is 7.8 at 95%, and the critical value is 33.962. Therefore, the null
is rejected, as there is a significant difference between forest acreage in the
north and the south.
 |
| Table 1 |
The second chi-squared test (Table 2) was to
determine whether or not the distribution of deer gun licenses was bounced
between the northern and southern parts of Wisconsin. For this test, the null
hypothesis was that there was no difference between the expected distribution
of gun licenses and actual distribution. The alternate hypothesis was that the
expected distribution of gun licenses was different from the actual
distribution of gun licenses. After calculating the chi-square test, the test
statistic is 7.8 at 95%, and the critical value is 4.399. As the critical value
is less then the test statistic, I am unable to reject the null.
 |
| Table 2 |
The third chi-squared test (Table 3) was to
determine whether or not the percentage of the population that deer hunt is
equally distributed between the northern and southern parts of the state. For
this test, the null hypothesis was that the percentage of the population that
hunts deer is randomly distributed across the state. The alternate hypothesis
was that the percentage of the population that hunts deer is not randomly
distributed across the state. The test statistic is 7.8 at 95%, and the
critical value is 16.428. As the critical value is greater than the test
statistic, the null is rejected.
 |
| Table 3 |
Conclusion:
When looking at map two, the distribution of
forest is very visibly skewed to the north, and the results of chi-squared test
one show this. These forests play a significant role in the cultural
differences between the northern and southern parts of the state, as there are
indicative of less agriculture and more of a reliance on the other forms of
income.
 |
| Map 2 |
When looking at map three, the distribution of
deer gun tags seems randomly distributed across the state, and the results of
chi-squared test two supports this. I chose this result because of how it did
not fit my preconceived notion of the distribution of deer tags throughout the
state.
 |
| Map 3 |
When looking at map four, the percentage of
the county population with deer gun tags in the north is visibly higher than
that in the south. This distribution is very different from the expected
distribution as seen in table 3. I chose this result because it helps to show
how much more of a cultural phenomenon deer hunting is in the northern parts of
Wisconsin then in the southern parts of the state, as a far greater percentage
of the population hunts in the north than in the south.
 |
| Map 4 |
