Part 1: t and z tests:
2. A Department of Agriculture and Live Stock Development in Kenya estimate that yields in a certain district should approach the following amounts in metric tons, (average based on data from the whole country) per hectare: groundnuts 0.5; cassava 3.70; and beans 0.30. The survey was of 100 farmers and these are the results.
Sample Mean Standard Deviation
Ground Nuts 0.40 1.07
Cassava 3.4 1.42
Beans 0.33 0.14
The hypothesis testing for Groundnuts is two-tailed test with the Confidence level of 95%.
For Groundnuts I used a z test because the amount of samples is over 30.
Null Hypothesis: There is no significant difference between the mean and the hypothesized mean.
Alternative Hypothesis: There is a significant difference between the mean and the hypothesized mean.
Conclusion: We fail to reject the null hypothesis because there is no significant difference in the yields between actual and the hypothesized mean.
The probability is 82.38% that there will be similar yields next year.
The hypothesis testing for Cassava Nuts is a two-tailed test with a Confidence level of 95%.
For Cassava Nuts I used a z test because the amount of samples is over 30.
Null Hypothesis: There is no significant difference between the mean and the hypothesized mean.
Alternative Hypothesis: There is significant difference between the mean and the hypothesized mean.
Conclusion: We reject the null hypothesis because there is a significant difference between the actual and the hypothesized yields as they are lower than the confidence level.
The probability is 98.26% that there will be similar yields next year.
The hypothesis testing for Beans is a two-tailed test with a Confidence Level of 95%.
For Beans I used a z test because the amount of samples is over 30.
Null Hypothesis: There is no significant difference between the mean and the hypothesized mean.
Alternative Hypothesis: There is a significant difference between the mean and the hypothesized mean.
Conclusion: We reject the null hypothesis because there is a difference between the actual and hypothesized mean of beans. The yields are higher than the confidence level.
Wilderness Parks
A survey of the all the users of a wilderness park was taken in 1960 revealed that the average number of person per party at the park was 2.8. In a random sample of 25 parties in 1985, the average was 3.7 with a standard deviation of 1.45.
This survey was done with a with a one tailed test with a Confidence level of 95%.
For the Wilderness Parks I used a t-test because the sample is less than 30.
Null Hypothesis: There is no significant difference between the mean and the hypothesized mean.
Alternative Hypothesis: There is a significant difference between the mean and the hypothesized mean.
Conclusion: We reject the null hypothesis because there is a significant difference in the mean and the hypothesized mean. The amount of people per party in 1980 is higher than in 1969. These results are not totally the same as the first survey in 1960 was of all users but the survey in 1980 was of a sample. It is possible that the sample may just have more people than another sample would have. I feel if this was done again with another 25 random people the results could possibly be much different, possibly more people per party or even less depending on the sample.
The probability is 1.711 or 83%.
Part II. Chi-Squared Testing
This is a an analysis of what is considered "Up North." I made a map of Wisconsin from the United States Census Bureau, America Factfinder site. I then decided, based on the location of Highway 29, which counties I would consider North and which ones I chose to be South. I then assigned the 1 and 2 values to the counties in order to do the Chi-square calculations.
I decided to make Clark County part of the south even though it was more northern than most of the others I chose. I chose this based on the location of Highway 29. I chose to have Marathon County to be in the North even though it is cut pretty close to in half by Highway 29.
Next I chose the three variables to conduct a Chi-squared testing. The variables I selected beaches, picnic areas and bike trails. The following maps will show the results of the analysis of the variables and show the location of the variables on the maps.
Location of Bike Trails.
This map shows the dark blue area is 100 bike trials or more. There are three counties in the south that have 100 or more, Dane, Milwaukee and Waukesha. The northern part of the state only has one county, Door County that has over 100. The next color on the legend is the green (50-99) which also has more counties in the south. The dark red or rust color shows the amount of counties that have (25-49) which by the map shows it is really close to even on the number of counties. The last one is the light blue which is (0-24) bike trails per county. This category is also judging from looking at the map to be about the same in the north as in the south.
Below is the Chi-squared results. I opened the SPSS and imported the dbase file exported from ArcMap, then I chose Analyze, Descriptive reports, Crosstabs and then I made sure to check the box on the Chi-square box the continue. This is the results of this process.
The Chi-squared tests shows the following results.
1.00
-.507
---------
0.493 X 100= 49.3%
The Pearson Chi-Squared value is 2.329 with 3 degrees of freedom.
Public beaches by county.
Below is the Chi-squared results. I opened the SPSS and imported the dbase file exported from ArcMap, then I chose Analyze, Descriptive reports, Crosstabs and then I made sure to check the box on the Chi-square box the continue. This is the results of this process.
The Chi-squared tests shows the following results.
1.00
-.507
---------
0.493 X 100= 49.3%
The Pearson Chi-Squared value is 2.329 with 3 degrees of freedom.
Public beaches by county.
This maps shows the amount of public beaches per county. The purple counties signify counties with 20 or more public beaches. Door county is in the north and Kenosha on the bottom right of the map and Dane slightly north west of it are the two counties in the south that has the most public beaches. The next amount is the green with (8-13) public beaches and just judging by the colors on the map there are many more counties with 8-13 public beaches per county in the north. Next is the blue counties which is 5-7 beaches per county. It appears in the map to be evenly distributed across the state with the 5-7 category. The last is the pink and it appears that there are more of the 0-4 public beaches in the south. The northeastern part of the state appears to have the most public beaches in the state.
The results of this chart were achieved with the same process as above.
Chi-squared test shows the following results.
The results of this chart were achieved with the same process as above.
1.00
- .07
------------
.93 X 100= 93%
Picnic areas by county.
This map shows the amount of picnic areas per county. The dark blue areas represent the counties that have 100 or more picnic areas per county. According to the map all of the areas with 100 or more are in the south, the southeast to be more precise. The next color is the bright green (50-99) picnic areas per county, most of these are in the south as well, there are a few just north of 29 but none in the northern most part of the map. The next category of color is the light blue (25-49) appears to be pretty evenly distributed across the state. The last color is the teal blue which is (0-24) picnic areas. The category is mostly in the northern part of the state.
The results of this chart were achieved the same as above.
1.00
-.021
------------
0.979 X 100= 97.9%
We reject the null hypothesis because there is a significant difference in the amount of picnic areas in the south compared to the north.
Conclusion: Up -North is a relative term to the person who is doing the testing. It can be based off many different criteria. Highway 29 was chosen in this case as the line dividing the north and south. The maps illustrate the number of bike trails, beaches and picnic areas. The only county in the north that had a significant amount of each of these categories is Door County. Door County is located on the lake so it has a lot of recreational activities and it is a much more visited areas than many of the other counties up north due to its location. The maps also show that the south has many more picnic areas and bike trails, this is most likely due to the fact that the southern part of the state is much more urbanized and populated. The northern part of the state does not have any large cities or tourist areas besides Door County.
- .07
------------
.93 X 100= 93%
Picnic areas by county.
This map shows the amount of picnic areas per county. The dark blue areas represent the counties that have 100 or more picnic areas per county. According to the map all of the areas with 100 or more are in the south, the southeast to be more precise. The next color is the bright green (50-99) picnic areas per county, most of these are in the south as well, there are a few just north of 29 but none in the northern most part of the map. The next category of color is the light blue (25-49) appears to be pretty evenly distributed across the state. The last color is the teal blue which is (0-24) picnic areas. The category is mostly in the northern part of the state.
The results of this chart were achieved the same as above.
1.00
-.021
------------
0.979 X 100= 97.9%
We reject the null hypothesis because there is a significant difference in the amount of picnic areas in the south compared to the north.
Conclusion: Up -North is a relative term to the person who is doing the testing. It can be based off many different criteria. Highway 29 was chosen in this case as the line dividing the north and south. The maps illustrate the number of bike trails, beaches and picnic areas. The only county in the north that had a significant amount of each of these categories is Door County. Door County is located on the lake so it has a lot of recreational activities and it is a much more visited areas than many of the other counties up north due to its location. The maps also show that the south has many more picnic areas and bike trails, this is most likely due to the fact that the southern part of the state is much more urbanized and populated. The northern part of the state does not have any large cities or tourist areas besides Door County.
No comments:
Post a Comment