Drug Content Assessment: Drug Concentrations Measured As A P

Question

Drug Content Assessmentdrug Concentrations Measured As A Percentage Drug content assessment: Drug concentrations (measured as a percentage) for 50 randomly selected tablets are provided in the accompanying table. The standard method of assessing drug content yields a concentrate variance of 9. The question asks whether the scientists at GlaxoSmithKline can conclude that the new method of determining drug concentration is less variable than the standard method. To answer this, a hypothesis test for the variance is appropriate. Specifically, a chi-square test for equality of variances can be employed to compare the variance from the new method against the known variance of the standard method. The null hypothesis, $H_0$, states that there is no difference in the variances, meaning the new method's variance is equal to the standard method's variance (which is 9). The alternative hypothesis, $H_1$, posits that the new method's variance is less than the standard method’s variance, indicating the new method is more precise. The first step involves calculating the sample variance from the data collected using the new method. Given the sample size $(n = 50)$ and the individual measurements, the variance is computed as: $$ S^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2 $$ where $x_i$ are the individual measurements and $\bar{x}$ is the mean of the sample. Next, the test statistic, which follows a chi-square distribution under the null hypothesis, is calculated as: $$ \chi^2 = \frac{(n - 1) S^2}{\sigma_0^2} $$ where $\sigma_0^2 = 9$ is the variance under the null hypothesis. This test statistic is compared to the critical value $ \chi^2_{\alpha, n - 1} $ at a chosen significance level $\alpha$ (often 0.05). Since the goal is to determine if the new method's variance is less, a one-tailed test is used, and the critical value is taken from the lower tail of the chi-square distribution. Utilizing the sample data, the calculated variance provided in the data,

Dr. Jack HW Helper · Accepted Answer

Introduction Evaluating the consistency and reliability of drug content assessments is vital in pharmaceutical quality control. Variability in measurements can lead to incorrect dosage, affecting drug safety and efficacy. Standard methods for assessing drug content often have known variability, and developing new methods with lower variance can significantly enhance reliability. This paper examines whether the new measurement method at GlaxoSmithKline demonstrates reduced variability compared to the established standard, employing statistical hypothesis testing. Background and Justification The pharmaceutical industry requires rigorous quality assurance protocols to ensure drugs meet specified standards. Variability in drug content measurements can stem from numerous sources, including instrument precision, operator differences, and methodological inconsistencies. Lower variability indicates higher reproducibility and accuracy, which are essential for regulatory compliance and consumer trust. The standard method's variance, known from previous studies, is 9, providing a benchmark for comparison. The primary goal is to assess whether the new method can achieve a statistically significant reduction in variability. Methodology The methodology involves a one-sample variance test, comparing the sample variance obtained from the 50 new method measurements against the known variance of 9. The hypotheses are formulated as: - Null hypothesis ($H_0$): The variance of the new method, $\sigma^2$, equals 9. - Alternative hypothesis ($H_1$): The variance of the new method is less than 9, i.e., $\sigma^2 The sample data yields a sample variance (\(S^2$). The test statistic follows a chi-square distribution: $$ \chi^2 = \frac{(n - 1) S^2}{\sigma_0^2} $$ where $n = 50$ and $\sigma_0^2=9$. The test is one-sided, focusing on whether the observed variance is significantly less than the benchmark. The significance level $\alpha$ is set at 0.05, and the critical chi-square

Drug Content Assessment: Drug Concentrations Measured As A P

Drug Content Assessmentdrug Concentrations Measured As A Percentage

Paper For Above instruction

Introduction

Background and Justification

Methodology

Results

Discussion

Conclusion

References