Statistical analysis in research is a critical tool that evaluates the significance of a statement held to be true of a studied phenomenon. Statistical analysis processes applied are known as statistical tests, and they vary with the nature of data collected and objective. The methodological framework has an impact on results. Analysis techniques and data collection are critical success factors (CSFs) on the reliability and credibility of findings in making an informed conclusion. Using sample data, the article illustrates the impact of a sample size to the "confidence interval estimate" of a statistical test. The analysis assumes that the data is random and with a normal distribution (Schmitz, 2012)
The objective of the study is to establish "how to sample proportion affect the confidence interval." Data used is from a poll on the President's performance in managing the financial market crisis. The poll results with a sample population of 1280 found 575 said they “approve or strongly approve” the President's actions. Research methodology establishes confidence interval for results at 95% and evaluates the effect of sample size if the results were based on a sample size of 2560 with an outcome of 1150 score index on “approve or strongly approve” (Schmitz, 2012).
Delegate your assignment to our experts and they will do the rest.
Data
| Observation 1 | N | Observation2 | N2 |
| 575 | 1280 | 1150 | 2560 |
Q1 Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population
Method: Binomial Distribution in Normal Approximation
Variance σ 2 = Nπ (1-π)
Where π = probability of an expected outcome
| Observation | N | π | Observation2 | N2 | π |
| 575 | 1280 | 0.45 | 1150 | 2560 | 0.45 |
| VARIABLE | Sample I | Sample II | |
| π | 0.45 | ||
| (1-π) | 0.55 | ||
| variance | 316.8 | 633.6 | |
| Stdev | =sqrtσ 2 | 17.80 | 25.17 |
| confidence-Coefficient | 0.95 | ||
| α | 0.05 | ||
| margin error | 0.9751 | 0.9751 |
Margin error = 0.9751 ≈ 1 because a voter/person cannot be accounted for like a fraction
Confidence interval for sample 1 at 95% confidence level = 575±1 = 574 – 576
Q2. If the same sample proportion was found in a sample twice as large-that is 1150 out of 2560-how, would this affect the confidence interval?
Margin error = ±1
From the data analysis results, if all other factors remain constant increase in sample size would not affect the results of the sample population.
If the sample size is significantly small, the margin error is large and statistically unacceptable as per scientific research methods principles. The sample size is a significant factor in statistical analysis on confidence interval through three parameters. The sample size affects the margin of error, power, and type II error, and the results' reliability. As the sample size increases, margin error reduces, reducing the chances of type II error and reliability of the statistical test results.
In conclusion, Data collection is an engaging activity that is time-consuming. An increase in sample size at some point can translate to high cost because it has no statistical or practical significance to results obtained.
Reference
Schmitz, A. (2012). Beginning Statistics. Retrieved from: https://2012books.lardbucket.org/pdfs/beginning-statistics.pdf
