Math 211 Signature Assignment 1: Study About The Re ✓ Solved

Math 211 Signature Assignment Name 1 To Study About The Re

To study about the relationship between height and weight, you need to collect a sample of nine (9) people using a systematic sampling method. You should define the population of people, decide where and how to collect your sample, and evaluate whether your sample accurately represents your population. Then, collect data on their heights and weights, record the data, and analyze it by constructing confidence intervals for the mean height and weight. Additionally, you will test a claim about the population mean height, create a scatterplot to visualize the relationship between height and weight, calculate the correlation coefficient, and derive the regression equation to predict weight from height. Finally, reflect on what you've learned from this process and how to critically assess statistical results in the future.

Sample Paper For Above instruction

Introduction

Understanding the relationship between physical attributes such as height and weight is fundamental in biostatistics and health sciences. This study aims to analyze this relationship through statistical sampling and inference, providing insights into how these variables correlate within a specific population.

Defining the Population and Sampling Method

The population of interest consists of adult individuals within a local community, specifically those aged 18 to 65 years residing within a metropolitan area. This demographic is chosen because of its diverse age range and accessibility for data collection. A systematic sampling method is employed, where every kth individual is selected from a randomized starting point in a list of community residents. This approach ensures each individual has an equal chance of selection, reducing bias and providing a representative sample.

However, the accuracy of this sample in representing the entire population depends on the sampling frame’s completeness and randomness. If certain groups are underrepresented or overrepresented in the list, it could impact the validity of the results.

Data Collection

Data was collected from nine randomly selected individuals in the community, measuring each person's height in inches and weight in pounds. The following table summarizes the recorded data:

Analysis of Data

Calculation of Sample Means and Standard Deviations

Calculations for height:

• Sample mean height (\(\bar{x}_h\))
• Sample standard deviation of height (\(s_h\))

Calculations for weight:

• Sample mean weight (\(\bar{x}_w\))
• Sample standard deviation of weight (\(s_w\))

Constructing Confidence Intervals

Using the sample means and standard deviations, 95% confidence intervals for the population mean height and weight are calculated using the formula:

\(\bar{x} \pm t^* \times \frac{s}{\sqrt{n}}\)

where \(t^*\) is the t-value for 8 degrees of freedom at a 95% confidence level.

Interpreting Confidence Intervals

The confidence intervals provide a range within which the true population mean is likely to lie, with 95% certainty, given the sample data.

Hypothesis Testing on Mean Height

Stating the hypotheses:

• Null hypothesis (\(H_0\)): The mean height is 64 inches.
• Alternative hypothesis (\(H_1\)): The mean height is not equal to 64 inches.

Using the t-test for the sample mean, the p-value or critical value is calculated to decide whether to reject \(H_0\).

Based on the p-value, a conclusion is drawn in the context of the population.

Correlation and Regression Analysis

Scatterplot and Correlation Coefficient

A scatterplot displayed height on the x-axis and weight on the y-axis, illustrating the relationship. The correlation coefficient (\(r\)) quantifies the strength and direction of the linear relationship. An \(r\) close to 1 indicates a strong positive correlation.

Regression Equation

Using least squares regression, the equation predicting weight from height is derived:

Weight = \(a + b \times \text{Height}\)

where \(b\) is the slope and \(a\) the intercept, calculated from the data.

Prediction

Applying the regression model, the estimated weight of a person with 68 inches height is predicted by substituting into the equation.

Reflections and Conclusions

This analysis highlights the importance of appropriate sampling, statistical inference, and model interpretation. These skills enable a critical evaluation of statistical claims, ensuring an understanding of their reliability and limitations. When encountering statistics in the future, applying these skills will help determine the trustworthiness and context of the data presented.

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