Create Confidence Intervals Related To The Inter

Create Confidence Intervals Related To The Inter

Assessment Descriptioncreate Confidence Intervals Related To The Inter

Assessment Description Create confidence intervals related to the interval and ratio-level data you collected. What is the best estimate of the population mean Develop a 95% confidence interval for the population mean. Develop a 90% confidence interval for the population mean. Develop a 98% confidence interval for the population mean. Interpret the confidence interval.

Create an individual Excel document for each of the required items. This is a continuation of the Data Collection assignment, Create Data Set Project, and Descriptive Statistics.

Paper For Above instruction

This paper aims to demonstrate the process of creating and interpreting confidence intervals for interval and ratio-level data obtained from a previous data collection effort. The primary goal is to estimate the population mean with varying degrees of confidence—specifically at the 90%, 95%, and 98% confidence levels—and to interpret these intervals in a meaningful statistical context. Such analyses are fundamental in inferential statistics, allowing researchers to estimate population parameters based on sample data with an associated level of certainty.

To begin with, the data collected previously consisted of measurements at the interval or ratio scale, which provide meaningful numerical differences and, in some cases, an absolute zero point. For this example, suppose the data consisted of the recorded heights of a sample of individuals. The sample size, mean, and standard deviation of these measurements are crucial parameters for constructing confidence intervals. Using these parameters, we can apply the formula for the confidence interval of the mean, which is given by:

CI = x̄ ± Z*(s/√n)

where:

- x̄ is the sample mean,

- s is the sample standard deviation,

- n is the sample size,

- Z* is the Z-value corresponding to the desired confidence level from the standard normal distribution.

For each confidence level—90%, 95%, and 98%—the appropriate Z-values are approximately 1.645, 1.96, and 2.33, respectively. These values are derived from the standard normal distribution and represent the cutoff points for capturing the specified proportion of data.

Applying these calculations, suppose the sample mean height is 170 cm, the standard deviation is 10 cm, and the sample size is 30. Then, the standard error (SE) is s/√n = 10/√30 ≈ 1.825. Calculating each confidence interval yields:

  • 90% CI: 170 ± 1.645 × 1.825 ≈ 170 ± 3.0, resulting in (167.0 cm, 173.0 cm)
  • 95% CI: 170 ± 1.96 × 1.825 ≈ 170 ± 3.58, resulting in (166.42 cm, 173.58 cm)
  • 98% CI: 170 ± 2.33 × 1.825 ≈ 170 ± 4.25, resulting in (165.75 cm, 174.25 cm)

Interpretation of these intervals suggests that, with the specified level of confidence, the true population mean height lies within the calculated range. As the confidence level increases, the interval widens, reflecting greater certainty but lower precision.

To perform these calculations practically, individual Excel spreadsheets should be created for each confidence level. These spreadsheets must include the sample data, the formulas for the mean and standard deviation, the calculation of the standard error, and the final confidence interval bounds. This approach ensures accuracy, transparency, and ease of updating if additional data are collected.

Furthermore, interpreting these confidence intervals in context involves understanding that they represent a range of plausible values for the population mean based on the sample data. For example, if the 95% confidence interval for average heights is (166.42 cm, 173.58 cm), one can state with 95% confidence that the actual average height of the population falls within this range. It is crucial to recognize that this does not imply that the population mean is equally likely to be any value within the range, but rather that the process of sampling and interval estimation has a specific confidence proportion over numerous repetitions.

In conclusion, constructing confidence intervals at different confidence levels provides essential insights into the precision and reliability of population parameter estimates. By following the outlined methodology and using an Excel spreadsheet for calculations, researchers can effectively communicate their findings and support decision-making based on statistical evidence.

References

  • Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (4th ed.). SAGE Publications.
  • Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences (8th ed.). Cengage Learning.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). W. H. Freeman & Company.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications.
  • Newbold, P., Carlson, W., & Thorne, B. (2013). Statistics for Business and Economics (8th ed.). Pearson.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
  • Lee, P. M. (2016). Statistical Methods for Data Analysis, with Applications in Business and Economics. Taylor & Francis.
  • Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the Behavioral Sciences (10th ed.). Cengage Learning.
  • Upton, G., & Cook, I. (2014). Oxford Dictionary of Statistcs (6th ed.). Oxford University Press.
  • Walpole, R., Myers, R., Myers, S., & Ye, K. (2019). Probability & Statistics for Engineering and the Sciences (9th ed.). Pearson.

Related Assignments