AP Statistics Test Page 1 Of 4 Planning A Study User Name

AP Statistics Test Page 1 of 4 Planning A Study User Name

Explain how you would carry out a test in a completely randomized experiment comparing a new drug to fish oil and a placebo, including how to ensure the randomness of the experiment and how to implement blocking to modify the design.

Describe a simulation approach to estimate the percentage of U.S. households that own at least one cat, using a random digit table to simulate the selection of households and performing three trials with clear procedures, then draw conclusions from these trials.

Identify a problem with sampling shoppers at two different stores for a survey on job satisfaction and suggest improvements to obtain more accurate data.

Paper For Above instruction

Introduction

Designing a robust experiment and conducting effective surveys are fundamental aspects of statistical research. Proper randomization and control methods help ensure valid and generalizable results. This paper explores the methodology for a clinical trial investigating a new drug, a simulation to estimate household characteristics, and an improved sampling strategy for a survey related to job satisfaction, illustrating critical concepts in experimental design and survey sampling.

Part 1: Carrying Out a Completely Randomized Experiment

The clinical trial proposed by Ace Pharmaceutical aims to evaluate the effectiveness of a new drug intended to lower cholesterol and blood pressure compared to fish oil and a placebo. To carry out this experiment in a completely randomized manner, first, all 300 volunteers must be randomly assigned to one of three treatment groups: the new drug, fish oil, and placebo. A random number generator or lottery method can be used to assign each participant, ensuring that each individual has an equal chance of being in any group, which eliminates selection bias.

Once participants are assigned, the next step is to administer the respective treatments under controlled conditions. It is essential to maintain the blindness of the trial—neither the participants nor the researchers should know which treatment each participant receives (double-blind design)—to prevent bias in treatment administration and outcome assessment. Data collection should follow standardized procedures, and the health outcomes related to cholesterol and blood pressure should be measured at predefined intervals.

Data analysis would involve comparing the results across the three groups using appropriate statistical tests, such as ANOVA, to determine if significant differences exist in the effectiveness of the treatments. This methodology ensures the internal validity of the experiment, attributing differences in outcomes to the treatments rather than extraneous factors.

Part 2: Ensuring Randomness in the Experiment

To ensure that the experiment is genuinely random, several steps must be followed. First, assigning subjects to treatment groups must be done purely by chance, such as using a computer-generated random number table or a randomization algorithm, which prevents systematic bias in group assignment. Verification of randomness can be achieved by checking the uniformity of the distribution of assignments and making sure no subgroup is disproportionately represented.

Furthermore, it is critical to implement procedures that prevent selection bias after initial randomization. For instance, allocation concealment, where the person responsible for enrolling subjects does not know the upcoming assignments, helps maintain the integrity of the random process. Additionally, documenting the randomization process transparently ensures reproducibility and credibility of the study.

Finally, blinding the experiment and training staff thoroughly on protocol adherence prevent unintentional introduction of bias, solidifying the randomness of the assignment process and minimizing biased influences on the outcome.

Part 3: Using Blocking to Improve Experimental Design

Blocking is a technique used to account for variability among experimental units by grouping similar units together before randomly assigning treatments within each group. In this scenario, blocking could involve stratifying volunteers based on factors known to influence cholesterol and blood pressure, such as age, gender, or baseline health conditions.

For instance, participants could be divided into blocks according to age groups: under 40, 40-60, and over 60. Within each age group, participants would then be randomly assigned to the three treatments. This design reduces variability attributable to age and enhances the precision of the treatment effect estimates.

The choice of blocking is justified when the blocking factor is believed to have a significant impact on the response variables, which in this case, are cholesterol and blood pressure. By controlling for these confounding variables, the experiment's statistical power improves, enabling clearer interpretation of the treatment effects.

Thus, blocking improves the experiment by increasing the accuracy and reliability of conclusions, especially when participants vary widely in characteristics that may influence the outcomes.

Part 4: Simulation to Estimate U.S. Household Cat Ownership

The objective is to estimate the proportion of U.S. households owning at least one cat using simulation and a random digit table. Assume the proportion is approximately 34%. The process involves defining coding rules for the digit table—such as assigning certain digits or digit ranges to indicate a household with or without a cat. For example, digits 0–3 may represent households owning cats, while digits 4–9 represent those without, based on the probability.

Each trial involves randomly selecting ten households by reading the digits in sequence. For clarity, one might assign two-digit pairs to each household: 00–33 indicates ownership; 34–99 indicates no ownership. Record each outcome, and repeat this process three times to perform three trials. During each trial, mark or record on the digit table which households are presumed to own cats based on the coding scheme.

After completing the three trials, calculate the proportion of households owning cats in each trial and then find the average across trials. This average provides an estimate of the percentage of U.S. households that own at least one cat, with a measure of variability derived from the three trials. This simulation embodies the principles of probabilistic sampling and helps understand the likely percentage based on the sample data.

Part 5: Addressing Bias in Sampling Shoppers at Different Stores

The sampling method described involves collecting data from shoppers exiting two distinct types of stores: a discount clothing store (store A) and a high-end boutique (store B). A potential problem with this approach is selection bias, which occurs because shoppers at these stores are not representative of the general population. Customers at a discount store may have different socio-economic statuses, lifestyles, or job satisfaction levels than those shopping at a high-end boutique, leading to biased results that are not generalizable.

To improve the sampling design, Kim and Tracy could employ stratified random sampling across multiple store types or locations, ensuring that all segments of the population are proportionally represented. Alternatively, they could select a random sample of households or individuals from a broader, randomized list rather than only shopping mall shoppers, which would reduce bias and improve the accuracy of their conclusions about job satisfaction.

Implementing a systematic sampling method, such as choosing every nth customer or using a random sampling frame that includes diverse demographic groups, would enhance the representativeness of the data. Moreover, combining data from various shopping venues, including both high-end and discount stores across different neighborhoods, would further improve the external validity of their survey results.

Conclusion

Proper experimental design, randomization, blocking, simulation, and sampling are vital techniques in conducting reliable research and surveys. By carefully applying these methods, researchers ensure validity, reduce bias, and produce results that truly reflect the population or phenomenon studied. The scenarios discussed emphasize the importance of rigorous planning and execution in statistical investigations to draw meaningful and accurate conclusions.

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