Abstract
This report contains the results of point estimate and confidence interval analysis for five variables obtained from the results of Springdale community shopping activities survey. The survey was conducted to determine the strengths and weaknesses of three shopping mall areas; Springdale Mall, Downtown Area and West Mall. The variables analyzed are general attitude towards Springdale, Downtown and West malls, and gender and marital status of the respondents. The maximum likely error for mean general attitude ranged from 170 to 0.189. On the other hand, maximum likely error for gender and marital was 0.003.
Introduction
Point estimation is a statistical technique used to find the value of a parameter from a distribution using data obtained from that distribution (Petkovic, 2006). A point estimate is reliable statistical guess or estimate of the value of a parameter in a population. In the analysis, sample mean was used point estimate of population mean.
Point estimates were used to calculate confidences interval of the values of the variables. Confidence interval in statistics refers to a range of values that is likely to contain the value of a parameter in population (Blischke, Murthy & Wiley InterScience, 2000). The confidence interval for population mean was calculated using the sample mean and standard deviation. Standard deviation, sample size and z-score were used to calculate maximum likely error.
Analysis
- Springdale Mall
The point estimator = mean
Ө =
= 3.813
Standard deviation = 1.064
The z-score for 95% confidence level is 1.96
Sample size n = 150
Confidence interval = ± z.
3.813 ± [1.96 X (1.064 ÷ 12.247)
3.813 ± 0.170
3.647 to 3.987
The average attitude towards Springdale falls between 3.643 and 3.983
Maximum possible error is 0.170
- Downtown
The point estimator = mean
Ө =
= 3.407
Standard deviation = 1.124
Confidence interval = ± z.
- ± [1.96 X (1.124 ÷ 12.247)
3.407 ± 0.180
3.227 to 3.587
The average attitude towards Downtown falls between 3.227 and 3.587
Maximum possible error is 0.180
- West Mall
The point estimator = mean
Ө =
= 3.287
Standard deviation = 1.183
Confidence interval = ± z.
- ± [1.96 X (1.183 ÷ 12.247)
3.287 ± 0.189
3.098 to 3.476
The average attitude towards Downtown falls between 3.098 and 3.476
Maximum possible error is 0.189
- Population proportion of males
Point estimator = proportion of males, p.
64/150 = 0.427
Proportion of females, q
86/150 = 0.573
Confidence interval =.
0.427 ± 1.96 X (0.427X0.573 ÷ 150)
0.427 ± 0.003
The population proportion of males falls between 0.424 and 0.430 or 42.4% and 43.0%.
The maximum error is 0.003 or 0.3%
- Population proportion of single or other
Point estimator = proportion of single or other, p.
83/150 = 0.553
Proportion of married, q
67/150 = 0.447
Confidence interval =.
0.553 ± 1.96 X (0.553X0.447) ÷ 150)
0.553 ± 0.003
The population proportion of males falls between 0.550 and 0.556 or 55.0% and 55.6%.
The maximum error is 0.003 or 0.3%
Conclusion
The maximum likely error for general attitude towards Springdale, Downtown and West were 4.46%, 5.28% and 5.75% respectively. It was noted that the error was reduced with increase in mean. Meaning that, the variability of data was higher for shopping areas that community residents did not like. The maximum likely error for proportion for gender and marital status was equal, 0.03%.
References
Blischke, W. R., Murthy, D. N. P., & Wiley InterScience (Online service). (2000). Reliability: Modeling, prediction, and optimization. New York: Wiley.
Petković, M. (2008). Point estimation of root finding methods. New York: Springer.
