Quantitative Analysis of Student Math Study Hours: Confidence Intervals

1 INTRODUCTION TO QUANTITATIVE ANALYSIS: CONFIDENCE INTERVALS Valeria M. Díaz García Walden University RSCH-62101 Quant Reasoning & Analysis December 24, 2023 One-Sample Statistics

2 N Mean Std. Deviation Std. Error Mean Hours spent on math homework/studying in typical school week. 4565 2.58 1.593 .024 Confidence interval (CI) is defined by Frankfort-Nachmias (2020) as a range of values defined by the confidence level within which the population parameter is estimated to fall. When we use confidence intervals to estimate population parameters, such as hrs spent on math homework/studying in typical school week, we can also evaluate the accuracy of this estimate by assessing the likelihood that any given interval will contain the mean. This likelihood, expressed as a percentage or a probability, is called a confidence level. Confidence intervals are defined in terms of confidence levels. Thus, by selecting a 95% confidence level, we are saying that there is a .95 probability—or 95 chances out of 100—that a specified interval will contain the population mean. The tables below show the CI of hours spent on math homework or studying in a typical school week, the population, the mean, std. deviation and error. One-Sample T test for a 95% confidence interval One-Sample Test Test Value = 0 t df Significance Mean Difference 95% Confidence Interval of the Difference One-Sided p Two-Sided p Lower Upper Hours spent on math homework/studying in typical school week 109.260 4564 .000 .000 2.577 2.53 2.62 To calculate CI, we need to know the central tendencies of the variable, and standard deviation. The equation is as follow Confidence Interval=Mean ± (critical t-Statistic× Standard

3 Error). In the equation, "Mean" refers to the sample mean, which is the average value of the data in the sample. The "critical t-Statistic" represents the critical value from the t-distribution, which is based on the desired level of confidence and the degrees of freedom associated with the sample. The "Standard Error" is a measure of the variability or dispersion of the sample data. To calculate the confidence interval, you take the sample mean and add or subtract the product of the critical t-Statistic and the Standard Error. This accounts for the uncertainty in estimating the true population parameter based on the sample. His is equal to 2.58+0.04704= 2.62 and 2.58- 0.04704= 2.53. In the HS long study dataset, the variable "hours spent on math homework or studying in a typical school week" (HSMH) exhibits a 95% confidence interval of (2.53, 2.62). This confidence interval suggests that, based on the data collected, we can be 95% confident that the true population mean of hours spent on math homework or studying falls within this range. In other words, the average amount of time students spends on math homework or studying in a typical school week is estimated to be between 2.53 and 2.62 hours. X1SES (T1 socio-economic status composite) mean. Statistics T1 Socio-economic status composite N Valid 5422 Missing 503 Mean .0558 Median -.0137 Mode -.78 Valid 5422 Missing 503

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4 .0558 This is aligned when examining the central tendency of the variable, we find that the mean is 2.58 hours, the median is 2.00 hours, and the mode is 2. This indicates that the distribution of hours spent on math homework or studying is slightly positively skewed, as the mean is slightly higher than the median and mode. Based on the provided information, a potential social change implication could be the need for targeted interventions and support systems to ensure equitable access to educational resources and opportunities. The wide range of variation in the time students spend on math homework or studying suggests disparities in resources, support, and educational environments. Some students may have limited access to resources or face barriers that prevent them from dedicating sufficient time to studying, potentially impacting their academic performance and future opportunities. By recognizing and addressing these disparities, educational institutions and policymakers can work towards creating a more inclusive and supportive learning environment for all students, regardless of their individual circumstances. This may involve implementing initiatives such as after-school programs, tutoring services, or resource allocation strategies to ensure that students have equal opportunities to succeed academically.

5 References Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications. Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.

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