Easy Statistics Project Sample
In

### Introduction

This research was conducted on 10th December, 2013 at the parking bay of the college. The aim was to study the vehicles that are present in both the students' and the faculty parking lots. Special emphasis was put on the model of the vehicle in order to ascertain its country of origin. This would then form the basis of analysis and conclusion.

### Methodology

Cross-sectional study design was used to collect data at one point in time. One day was dedicated to data collection in order to avoid sampling bias that would be related to double counting of vehicles. Only the vehicles that were present at the parking lot were studied. The study population consisted of all the vehicles at the parking lot. There were 87 vehicles present at the parking lot. The study area, being the parking lot, was purposively selected to provide information to the study.

Simple random sampling was used to select the sample size that consisted of 40 cars. Of the sample size, students owned 20cars whereas 20 cars belonged to the faculty. All the cars were numbered from in ascending order after which small pieces of paper were made to represent each car. The papers were picked one at a time without replacement in order to obtain the sample size. For each paper picked, the car represented by that number was studied. Data collection was expedited through a data collection sheet as well as a short questionnaire that was filled by the owner of the vehicle. Data was then analyzed for measures of central tendency, spread, and disseminated through a written report.

### Hypotheses

i. Students and faculty have an equal proportion of foreign cars.

ii. Majority of the cars are owned for a maximum of 2 years.

Data

 Student's Parking Lot Number of Car Duration owned(Years) Model Country 1 1 Mercedes Benz Germany 2 3 Mercedes Benz Germany 3 2 Toyota Japan 4 1 Honda Japan 5 3 Volvo Sweden 6 1 Range Rover UK 7 1 Volkswagen Germany 8 0.5 Chevrolet USA 9 0.75 Toyota Japan 10 0.36 Toyota Japan 11 0.24 Toyota Japan 12 1 Mercedes Benz Germany 13 2 Hummer USA 14 3 Honda Japan 15 3 Hummer USA 16 2 Toyota Japan 17 1 Toyota Japan 18 2 Toyota Japan 19 2 Chevrolet USA 20 2 Toyota Japan Mean duration 1.5925 Standard deviation 0.925617148 Variance 0.856767105

 Faculty Parking Lot Number of Car Duration owned(Years) Model Country 1 2 Volkswagen Germany 2 4 Volkswagen Germany 3 2 Hummer USA 4 3 Hummer USA 5 2 Volkswagen Germany 6 1 Mercedes Benz Germany 7 1 Chevrolet USA 8 1 Mercedes Benz Germany 9 1 Range Rover UK 10 4 Volkswagen Germany 11 1 Range Rover UK 12 5 Range Rover UK 13 1 Hummer USA 14 1 Toyota Japan 15 2 Toyota Japan 16 1 Hummer USA 17 1 Mercedes Benz Germany 18 1 Volvo Sweden 19 1 Volkswagen Germany 20 1 Chevrolet USA Mean duration 1.8 Standard deviation 1.23969436 Variance 1.536842105

### Summary of the Findings

The mean duration of time for which students have owned cars is 1.59years while that of faculty is 1.8years. This research can be assumed to have a 95% confidence level factoring in the margin of error that is committed during sampling. We will use Z-statistics in computing the confidence interval. The mean duration of all the cars is 1.695years. The confidence interval is therefore computed as follows:

Standard deviation = 1.547 years

95% Confidence interval = Point estimate of the mean +/- Z X Standard deviation/√Sample size

Z value = 1.96

95% Confidence Interval = 1.695 +/- 1.96 X 1.547/√40

95% Confidence Interval = 1.695 +/- 0.48

Upper Limit = 1.695 + 0.48 = 2.175years

Lower Limit = 1.695 - 0.48 = 1.215years

We are therefore 95% confident that the mean duration that each car will be held is between 1.215years and 2.175years.

The proportion of the students that own foreign cars is 80% while 70% of the faculty own foreign cars. We can compute the 95% confidence interval for the difference in proportion means.

95% Confidence interval = Difference +/- Z X √ (p1q1/n1 +p2q2/n2)

95% Confidence Interval = (0.8-0.7) +/- 1.96 X √ (0.8 X 0.2/20 + 0.7 X 0.3/20)

95% Confidence Interval = 0.1 +/- 0.27

Upper Limit = 0.37

Lower Limit = -0.17

We are 95% confident that the difference in proportions ranges between -0.17% and 0.37%. This difference is thus not significant since the range contains a zero.

### Conclusion

The students and the staff thus do not have the same proportion of foreign cars. This disqualifies the first hypothesis while the second is also disqualified since the mean number of years a car can be owned exceeds 2years with and upper limit of 2.175years.