# the population, sample size, and data collection methods appropriate for your problem statement and research question. a 1,050- to 1,400-word paper describing how you will select your target population; your sample size; and your data collection methods. Include the following information in your paper: (Note: what you are doing here is putting more meat on the bones of your presentation in the previous week, but just in narrative form). the Assignment Files tab to submit your assignment.

Title: Population, Sample Size, and Data Collection Methods in Research Study

Introduction:
In this paper, we will discuss the selection of the target population, sample size determination, and data collection methods for our research study. These aspects are crucial as they directly influence the validity, reliability, and generalizability of the findings. By carefully considering these factors, we aim to ensure a representative sample and to gather high-quality data that allows for meaningful analysis and interpretation.

Selecting the Target Population:
The target population represents the group of individuals to which we want to generalize the research findings. Focusing on our problem statement and research question, it is important to identify the population precisely. Our research aims to explore the impact of various teaching methods on the academic performance of high school students in mathematics. Therefore, the target population for our study will be high school students across different educational institutions, representing varying socioeconomic backgrounds and geographical regions.

To ensure a broad representation, we will adopt a stratified random sampling technique. This technique involves dividing the population into relevant strata based on specific characteristics, such as grade level, socioeconomic status, and school type. We will then randomly select participants from each stratum, proportionate to its size, to achieve a diverse sample that accurately reflects the overall target population.

Determining Sample Size:
Selecting an appropriate sample size is crucial to ensure the reliability and statistical power of the study. There are various factors to consider when determining sample size, including the desired level of precision, statistical significance, and anticipated effect size. Moreover, the research design and resources available also influence the sample size determination.

In our study, we will adopt a quantitative approach and utilize a randomized controlled trial design to compare the effectiveness of different teaching methods. Since no preliminary effect size estimates are available for comparison, we will base our sample size calculation on conservative assumptions. However, given the wide variability in effect sizes reported in previous research, we will conduct a power analysis to estimate an appropriate sample size.

To conduct the power analysis, we will specify a significance level (alpha), power (1 – beta), and the minimum detectable effect size. The alpha level will be set at 0.05, implying a 95% confidence level, and the power will be set at 0.80 to minimize type II error. The minimum detectable effect size will be estimated based on prior research examining similar variables. This analysis will guide us in determining the required sample size to achieve sufficient statistical power.

Data Collection Methods:
To gather data for our study, we will employ both primary and secondary data collection methods. The primary method will involve administering a survey to the selected participants to collect quantitative data related to their academic performance and their perceptions of different teaching methods. The survey instrument will be developed based on existing validated scales and will include Likert-scale questions to assess various dimensions of academic performance and teaching effectiveness.

Furthermore, we will also collect qualitative data through interviews with a subset of the participants, purposively selected to include those from different strata and diverse academic backgrounds. These interviews will allow us to gain a deeper understanding of students’ experiences, attitudes, and motivations towards various teaching methods and their impact on academic performance.

In addition to primary data collection, we will also utilize secondary data sources. These may include school records, such as previous academic performance scores, attendance records, and demographic information. This information will augment the survey data, providing a more comprehensive understanding of the factors influencing the academic performance of high school students.

Conclusion:
In conclusion, the selection of the target population, sample size determination, and data collection methods are critical components of a research study. By carefully selecting a representative target population, determining an appropriate sample size, and employing a combination of primary and secondary data collection methods, we aim to ensure the validity, reliability, and generalizability of our findings. This will allow for meaningful analysis and interpretation, presenting a robust understanding of the impact of teaching methods on high school students’ academic performance in mathematics.