Suppose You Are Conducting A Survey To Investigate Cholester

Suppose You Are Conducting A Survey To Investigate Cholesterol Levels

Suppose you are conducting a survey to investigate cholesterol levels of people living in Riverside, CA. Using this scenario, write an essay that explores the following issues(You may include equations if necessary). 1. How would you collect the survey data? (Make sure you justify your procedure using relevant statistical theory and concepts) 2. How would you apply the hypothesis test for one population mean to this case? 3. How would you prove that the mean value of cholesterol levels in Riverside, CA is not equal to 210? You should provide null and alternative hypotheses statements for this particular situation. Also, discuss whether you would use z or t statistics, and why. Finally, discuss under what circumstance you would reject or accept the null hypothesis. What is the statistical rationale for rejecting or failing to rejecting the null hypothesis in this case? Your justification should be based on the comparison of p-value and significance level. Note that this is a hypothetical scenario, and you can make up numbers, but your arguments should be based on appropriate statistical concepts and theory. Each student should be able to address above-mentioned issues, applying relevant statistical concepts and theory taught in week 4, to receive full credits. (minimum words requirement: 500 words excluding original questions and title)

Paper For Above instruction

To investigate the cholesterol levels of residents in Riverside, CA, a methodical sampling and data collection process is essential, grounded in sound statistical principles. A critical step involves designing a representative sampling strategy to ensure that the collected data accurately reflect the population's characteristics. It is ideal to utilize a simple random sampling method, where each individual in Riverside has an equal chance of being selected. This approach minimizes bias and guarantees that the sample estimates are unbiased representations of the true population mean. Alternatively, stratified random sampling could be employed if subgroups within the population, such as age or gender groups, are known to influence cholesterol levels. By dividing the population into strata and sampling from each subgroup proportionally, we increase the precision of the estimates. The sample size should be calculated based on the desired confidence level and margin of error, using the standard sample size formula: \( n = \left(\frac{z_{\alpha/2} \sigma}{E}\right)^2 \), where \(z_{\alpha/2}\) corresponds to the critical z-value for the confidence level, \(\sigma\) is the population standard deviation (or an estimate), and \(E\) is the margin of error. Ethical considerations, such as informed consent and data confidentiality, should also guide the data collection process. Data can be gathered through blood tests administered at healthcare clinics, mobile health units, or during community health events, with standardized procedures to ensure consistency and reliability across measurements.

Applying the hypothesis test for one population mean involves several steps. First, define the null hypothesis \(H_0: \mu = 210\), where \(\mu\) represents the true mean cholesterol level in Riverside. The alternative hypothesis could be two-sided \(H_a: \mu \neq 210\), indicating an interest in determining if the mean differs from 210. Once data are collected, calculate the sample mean (\(\bar{x}\)) and sample standard deviation (\(s\)). Depending on the known population variance and sample size, select the appropriate test statistic: a z-test or t-test. Typically, since the population standard deviation is unknown in real-world scenarios and sample sizes are often small, the t-test is more appropriate. The t-statistic is calculated as: \( t = \frac{\bar{x}- \mu_0}{s / \sqrt{n}} \), where \(\mu_0 = 210\) is the hypothesized mean. Using the t-distribution accounts for additional uncertainty when the population variance is unknown.

To evaluate the hypothesis, compare the calculated p-value with a predetermined significance level (\(\alpha\)), commonly set at 0.05. If the p-value is less than \(\alpha\), reject the null hypothesis, concluding there is statistically significant evidence that the mean cholesterol level differs from 210. Conversely, if the p-value exceeds \(\alpha\), fail to reject the null, suggesting insufficient evidence to claim a difference exists. For instance, if the sample mean is 215 with a standard deviation of 30, a sample size of 50, the t-statistic would be calculated, and the p-value derived accordingly. Suppose the p-value is 0.03; since 0.03

The decision to reject or not hinges on the p-value comparison as well as the context. If we reject \(H_0\), it indicates that the observed sample provides enough evidence to conclude that the true mean differs from 210, which could influence public health policies. On the other hand, failing to reject \(H_0\) suggests that any observed differences could be due to sampling variability rather than a true difference in the population means. The choice between z and t statistics depends primarily on whether the population variance is known; in most practical situations, especially with small samples, the t-test is preferred due to the unknown population standard deviation. Additionally, the significance level (\(\alpha\)) indicates the threshold for establishing statistical significance; a lower \(\alpha\) (e.g., 0.01) makes the test more conservative, reducing the likelihood of Type I errors (false positives). It is important to interpret these statistical results within the broader context of health implications and consider potential Type II errors (failing to detect a true difference) in absence of sufficient sample size or power.

References

• Agronow, D. (2019). Foundations of Statistics. 4th Edition. McGraw-Hill Education.
• Casella, G., & Berger, R. L. (2002). Statistical Inference (2nd ed.). Duxbury Press.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Hogg, R. V., McKean, J. W., & Craig, A. T. (2019). Introduction to Mathematical Statistics. 8th Edition. Pearson.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. 9th Edition. W. H. Freeman.
• Rice, J. (2007). Mathematical Statistics and Data Analysis. Duxbury Press.
• Schmidt, F. L., & Hunter, J. E. (2015). Methods of Meta-Analysis: Correcting Error and Bias in Research Findings. Sage.
• Snedecor, G. W., & Cochran, W. G. (1989). Statistical Methods. 8th Edition. Iowa State University Press.
• Weiss, N. A. (2018). Introductory Statistics. 10th Edition. Pearson.
• Zar, J. H. (2010). Biostatistical Analysis. 5th Edition. Pearson.