Lab 3 - Significance Testing

1.

2. Ground Nuts
Probability: 35.24
z Value: -.9346

Fail to reject null hypothesis because it lies in the range of normal distribution.

Cassava
Probability: 0.0348
z Value: -2.1127

Reject the null hypothesis. -2.1127 falls too far away from the normal distribution of -1.96

Beans
Probability: 0.324
z Value: 2.1429

Reject null hypothesis. The samples are too different.

There are a few similarities amongst the data including 2/3 data sets fall outside of the significant range. As far as differences go each data set had a completely different Z-Score. This shows that among the three different crops there are some very different amounts.

3. Null Hypothesis: With a 95% confidence interval it shows there is not a difference between the average number of people per party comparing 1960 and 1985.

Probability:
1960: 2.8
1985: 3.7 (Sample size: 25)

T Test
(3.7 – 2.8) / (1.45/sqrt 25) = (0.9)/(0.29) = 3.1034
df=25-1=24

1.711

There is a significant difference between the 1985 sample and the 1960 party size meaning the null hypothesis is rejected.




Part II                                                       Defining Up-North

     The folks at the Wisconsin Tourism Board have asked me to do some research and help them define what "Up-North" means, where "Up-North" is and what people primarily do while there. Using a data set provided to me from them I will create some maps hopefully helping them out and elaborating on the concept of "Up-North."

     The first step was determining which counties were considered "Up-North" and what weren't. We determined any county with at least 50% of its area north of HWY 29 could be considered "Up-North" (Figure 1)


Figure 1 - State map showing what area is considered "Up-North" and "Down-South"

     Each county was given a value "1" or "2" depending on its location on the map, this list made working with the data easier and help determined which counties were considered "Up-North" or not.

      To show the tourism board a break down of where the majority of the State's population lived I also made them a map showing population by county. (Figure 2) This is helpful because as we know tourism often means travel is involved, and in the case of Wisconsin and "Up-North" the best tourist spots do not necessarily mean they are the highest populated places all year round.

     Comparing (Figure 1) and (Figure 2) you can see that "Up-North" counties primarily are those with the smallest populations where as the southern part of the state has the most residents.

     When doing a Google search for "Up-North Wisconsin" you get a plethora of results but one thing most of them have in common is that they involve being outside. With that being said, I focused on activities that are outside and appeal to large amounts of people. There are so many activities and variables that makeup "Up-North" but three I focused on was the Number of Public Boat Launches, Fishing Licenses Sold, and Bow Licenses Sold. The Travel Wisconsin has sections for all three of these activities and when "Up-North" comes up in conversation it is mostly related to boating, fishing, hunting, atving, snowmobiling, and staying at a cabin or campground while doing those activities.

     The first variable I chose to explore was the number of Public Boat Launches in Wisconsin. (Figure 3)

Figure 3 - Number of Boat Launches by County

     Using the data provided to me I broke the number of boat launches in to 5 different classes and represented them with varying shades of blue. The number of boat launches in a county is a good differentiator between North and South because people may associate with taking their boats "Up-North" for a weekend away. As the figure above shows the majority of boat launches in the state are in what we consider "Up-North."

     The next variable I chose to explore was the number of bow hunting licenses sold in the state of Wisconsin. (Figure 4)



Figure 4 - Bow Licenses Sold by County

     It is pretty commonly thought that in the State of Wisconsin there are a lot of bow hunters and by looking at the map we can certainly see that is true. However, the map also shows that the majority of licenses sold are not in what we consider "Up-North." If we compare this map to our state population map you may see some similarities. The counties with higher populations also sold higher amounts of licenses. This is makes sense because it does not necessarily mean that you will be hunting in the same county as where you purchased the license. If that was the case there would be a lot of urban hunting in the south east corner of the state. A possible explanation for this is that many hunters who live in the southern portion of the state also own land "Up-North" where the population is lower and there is by far more open land to hunt. (Figure 5)

Figure 5 - Forest Land in Acres


     The last variable I selected was the number of fishing licenses sold by county. (Figure 6)

Figure 6 - Fishing Licenses Sold by County



     Looking at the map you can see once again fishing licenses are sold much like bow hunting ones are. This makes sense because of the large populations of people that reside in those counties. By looking at (Figure 3) we can see there is a high demand for boat launches "Up-North", people are fishing off a percentage of these boats so it is not outlandish to assume some boat traffic is coming from the south and people are spending their time on the water fishing.

      Along with making the maps I also did a set of Chi-Square tests using a program called IBM SPSS Statistics. To do so, I exported the data from ArcMap and inputted them in to SPSS. Using SPSS calculating Chi-Squares for each set of variables is quick and easy. The test results are below.

Chi-Squared Boat Launch Results

Chi-Squared Bow License Results

Resident Fishing License Result

     Looking at the results of the Chi-Square test gives us an idea of whether the data is within the expected and observed frequency. Basically it equates to whether the variable is just as likely to occur "Up-North" or "Down-South".

     If the results are a null hypothesis that means there is no difference between the expected and observed frequency. Meaning there is just as likely of a chance something happens "Up-North" as there is "Down-South". If we have an alternate hypothesis that means the variable is more likely to occur either in the North or South.

     For the number of Boat Launches we fail to reject the null hypothesis, there is not enough variance either way to say there is a difference.

     For Bow Licenses, looking at the Chi-Squared test we fail to reject the null hypothesis.

     As far as the Resident Fishing Licenses go, the Chi-Squared test scored 0.276 which only has a confidence value of 72.4% . With that being said we fail to reject the null hypothesis, this means there is not enough variance either way to say a certain side has more of a difference.

Final Thoughts:

     With the above being said, there is certainly a stigma attached to "Up-North" and nobody can argue that there are a lot of activities to do while there. Wisconsin is a place full with opportunities to do things outside. With the above results you can see there may not be a way to discern "Up-North" from "Down-South" based purely off of individual activities and everyone's "Up-North" can mean something else. My "Up-North" is hunting, fishing, staying at our cabin, near family and my Grandparent's Ice Cream Shoppe.