Lab 3: Significance Testing

Part 1: T & Z Tests

Below are some terms and operations that are crucial to understand what was done later in the lab. Calculations of the data and terminology is crucial to determine the differences between Northern and Southern Wisconsin.

	Interval Type	Confidence Level	n	Sig. Level	z or t	z or t value
A	Two Tailed	90	45	0.05	Z	pos or neg 1.65
B	Two Tailed	95	12	0.05	T	pos or neg 2.201
C	One Tailed	95	36	0.05	Z	1.65
D	Two Tailed	99	180	0.01	Z	pos or neg 2.58
E	One Tailed	80	60	0.2	Z	2.06
F	One Tailed	99	23	0.01	T	2.5
G	Two Tailed	99	15	0.01	T	pos or neg 2.997

A Department of Agriculture and Live Stock Development organization in Kenya estimate that yields in a certain district should approach the following amounts in metric tons (averages based on data from the whole country) per hectare: groundnuts. 0.5; cassava, 3.70; and beans, 0.30.  A survey of 100 farmers had the following results:

 μ          σ

            Ground Nuts   0.40     1.07

            Cassava            3.4       1.42

            Beans              0.33     0.14

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

b.      Be sure to present the null and alternative hypotheses for each as well as conclusions

c.       What are the probabilities values for each crop? 

d.      What are the similarities and differences in the results

A.    Z-Score= Sample Mean – Country Mean/ (Standard Deviation/Sqrt(n))

Ground Nuts= -.9346

Fail to Reject

Cassava= -2.1127

Reject

Beans- 2.1429

Reject

B.     The Null hypothesis is that at a 95% confidence interval there is no difference between the averages of Kenya’s crop production in comparison to the other 100 sampled farmers. (ground nuts, cassava, beans)

The alternative hypothesis at a 95% confidence interval says there is a difference between the 100 sample farmer and the average crop production of Kenya.  (ground nuts, cassava, beans)

C.     Ground Nuts: -.9346 (No difference)

Cassava: -2.1127 (Difference)

Beans: 2.1429 (Difference)

D.    There are two similar things that I noticed when looking at the data that I calculated. Two out of the three data sets fell outside of the range that would have classified a difference. As far as Z- scores go the numbers varied more, -2.1127 was 2 standard deviations below the county average. Then -.9346 is also almost one standard deviation below the county average.  The final value of 2.1429 is over two standard deviations over the county average. Hence the differences that I spoke about in the opening sentence.

An exhaustive survey of all users of a wilderness park taken in 1960 revealed that the average number of persons per party was 2.8.  In a random sample of 25 parties in 1985, the average was 3.7 persons with a standard deviation of 1.45 (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)

b.      What is the corresponding probability value

A.    The Null hypothesis at a 95% confidence interval is that there is not a difference in the average number of people per party in 1960 in comparison to the 1985 sample.

The Alternative hypothesis at 95% confidence is that there is a difference in the number of people per party in 1960 in comparison to the 1985 sample.

B.     1960=2.8

Sample in 1985=3.7

Standard Deviation of 1.45

N(1985)=25

The corresponding probability value of 1.711 and the T-score of 3.1034 would lead us to reject the null hypothesis. What these numbers tell us is that there is a difference between the whole number of park users in 1960 compared to the 985 sample.

Part 2: What and Where is up North?

Introduction

      In this Lab we were tasked with determining what separates the north from the south in Wisconsin. I am sure my opinion of up north is much different than others. For the purpose of this assignment I used Highway 29 as my divider between north and south. The objective of this assignment is to learn how to calculate Chi-Square and then understand how it relates back to hypothesis testing. Next it was also important to understand how to relate a spatial output to the Chi- Square statistics and then to relate that all back to the real world. Then finally we have to make sense of all the numbers and calculation to relate this all back to geography. No matter where I looked there is no clear cut definition of Up North. Each individual persons perspective influences what they think is up north. To determine where up north is in Wisconsin I used three different data sets. I chose to use Non- Resident Gun licenses sold per county, Acres of Lake Per County and Non- Resident Fishing License sold per county.

Methods

      I first went onto the US Census site and brought in the Wisconsin counties. After the 72 counties were displayed in ArcMap I began to select all the counties that were north of highway 29 and all the counties south of Highway 29. If counties had 29 going through them, I separated them to the category that had the majority of the county. When looking at counties and trying to separate it my data may vary from others but I found 28 counties north of Highway 29 and 44 counties south of Highway 29. The counties north of 29 are a light shade of red while the counties south of 29 are a baby blue. Each of the other 3 variables that I used are represented by various numbers, for the counties they are just 1-4. It is sort of backwards in the aspect that 4 is the least and 1 is the most. We were provided SCORP DATA on the Q drive which was there to give us options into the data we wanted to map. Once we decided which ones we wanted to use, 3 separate joins were performed.

The Map above simply illustrates how I split the state for this lab. Red is Northern Wisconsin and Blue is Southern Wisconsin.

The Map above is a representation of the amount of non resident fishing licenses sold per county in the state of Wisconsin. The darker the green the more licenses sold in that county, then the lighter the color the less licenses sold. It is easy to see the cluster of dark green counties in the North West portion of the state and the again slightly East. I believe the reasoning behind this is that there is simply more species of fish such as walleye. Also fish number are higher, less pressured and generally speaking bigger. So this makes it an obvious attraction for out of county residents.

The Map above is a Map of the amount of Non Resident gun deer licenses sold per county in the State of Wisconsin. Very similar to the map of the non resident fishing licenses we see a similar pattern here. The NorthWest corner of the state is sell more tags than any other area. I believe this is because there is an immense amount of public land in that area. The Nicolet National Forest is close by, also many people own cabins up north for other recreational activities along with hunting.

The Map above is a Map of the amount of Acres of inland lakes that each county in the state of Wisconsin has. Here we see a slightly different trend than the previous two maps. the north doesn't necessarily dominate the map.