A Student Organization At A University Is Interested In Esti

A Student Organization At A University Is Interested In Estimating The

A student organization at a university is interested in estimating the proportion of students in favor of showing movies biweekly instead of monthly. A simple random sample (SRS) of 423 students revealed that 180 are in favor of showing movies biweekly.

Paper For Above instruction

The primary goal of this analysis is to estimate the proportion of students who prefer biweekly movie showings and to use this estimate to understand student preferences better. The sample data indicates that out of 423 students surveyed, 180 favor presenting movies every two weeks as opposed to once a month. This proportion can be employed to make inferences about the entire student population regarding their preferences for movie scheduling.

Introduction

This study focuses on estimating the proportion of university students favoring biweekly movie showings. By analyzing a random sample, researchers aim to determine whether the enthusiasm for more frequent movie presentations exists among the broader student body. This information could guide the student organization in decision-making related to event planning and resource allocation.

Estimating the Population Proportion

The sample proportion (p̂) is calculated as:

p̂ = number favoring biweekly / total sample size = 180 / 423 ≈ 0.425

This suggests that approximately 42.5% of students favor biweekly movie showings, based on this sample.

Confidence Interval for the Population Proportion

To extend this estimate to the larger population, a 95% confidence interval (CI) for the true proportion (p) is constructed. Using the formula:

CI = p̂ ± Zα/2 * √[p̂(1 - p̂) / n]

where Zα/2 = 1.96 for a 95% confidence level, p̂ = 0.425, and n = 423.

Calculations:

  • Standard error (SE) = √[0.425(1 - 0.425) / 423] = √[0.425 * 0.575 / 423] ≈ √[0.244 / 423] ≈ √[0.000577] ≈ 0.024
  • Margin of error (ME) = 1.96 * 0.024 ≈ 0.047

Therefore, the 95% CI is:

[0.425 - 0.047, 0.425 + 0.047] = [0.378, 0.472]

This interval indicates that with 95% confidence, the true proportion of students favoring biweekly movies lies between approximately 37.8% and 47.2%.

Hypothesis Testing

To support or refute the initial interest, hypothesis testing can be employed. For example, testing if the true proportion exceeds a certain threshold (say, 40%):

  • Null hypothesis (H0): p = 0.40
  • Alternative hypothesis (H1): p > 0.40

Using the sample data, the test statistic (z) is computed as:

z = (p̂ - p0) / √[p0(1 - p0) / n] = (0.425 - 0.40) / √[0.40 * 0.60 / 423] ≈ 0.025 / √[0.24 / 423] ≈ 0.025 / √0.000568 ≈ 0.025 / 0.0238 ≈ 1.05

Corresponding p-value (one-tailed) for z = 1.05 is approximately 0.147. Since the p-value exceeds 0.05, we do not reject the null hypothesis at the 5% significance level. This suggests insufficient evidence to conclude that more than 40% favor biweekly movies.

Interpretation and Conclusion

The analysis indicates that roughly 42.5% of students favor biweekly showings, with the 95% confidence interval ranging from approximately 37.8% to 47.2%. The hypothesis test results support the conclusion that there is not statistically significant evidence to affirm that more than 40% of students favor more frequent movie shows. This insight allows the student organization to make informed decisions about scheduling, knowing there exists substantial support but not overwhelming consensus for biweekly screenings. Further studies could explore factors influencing preferences or conduct similar analyses with larger or different samples.

References

  • Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data (4th ed.). Pearson.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2018). Statistics for Business and Economics (9th ed.). Pearson.
  • LaMorte, W. W. (2020). Confidence intervals and hypothesis testing. Boston University School of Public Health.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). Freeman.
  • Field, A., Miles, J., & Field, Z. (2012). Discovering Statistics Using R. SAGE Publications.
  • Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures (5th ed.). Chapman & Hall/CRC.
  • Hudson, L. N., et al. (2019). Survey analysis techniques. Journal of Educational Research, 112(3), 312-324.
  • Kirk, R. E. (2013). Experimental Design: Procedures for the Behavioral Sciences (4th ed.). SAGE Publications.
  • Rothman, K. J. (2014). Epidemiology: An Introduction. Oxford University Press.
  • UCLA Institute for Digital Research and Education. (2020). Confidence intervals in statistics. [Online].

Related Assignments