Biochar is a fine grain charcoal formed by burning biomass such as plant and tree waste in the absence of oxygen. It is thought that biochar can increase the fertility and health of soils used for agriculture. Researchers in Pakistan were interested in studying the effects of adding biochar to soil on the grain yield of regionally grown Mung bean. To study this, they selected 100 Mung bean seeds they had on hand at their laboratory. Each seed was planted in its own pot, and researchers used a coin flip to determine whether the seed’s pot had soil containing biochar or had soil without biochar. After the plants were fully grown, the researchers measured the grain yield of all 100 Mung bean plants. Is there an association between the use of biochar in soil and the grain yield of Mung bean plants? a. What are the observational units? b. List the variables in this data set and identify the type of variable (whether each variable is categorical or quantitative). c. Of the list of variables, what is the role of each variable (which would be the explanatory variable and which would be the response variable)? d. Identify if a given value is a statistic or a parameter. What is the appropriate notation? e. Identify and interpret the summary statistics given in the problem. f. What is the target population? g. Which types of sampling bias (response, non-response, selection, none) may be present in this study? Explain. h. Identify the type(s) of graph(s) that could be used to plot the given variable(s). i. Identify the variable(s) plotted in provided graphs. j. What is the study design? Is this an observational study or a randomized experiment? Explain. k. Identify a potential confounding variable and explain why that variable meets the definition of a confounding variable or explain why no confounding variables should be present. Use plots to explain why a variable may or may not be a confounding variable. l. Identify the scope of inference. i. Can we determine a causal relationship between variables? Explain ii. To which population can we generalize the results from this study? Explain. m. What is the purpose of random sampling? n. What is the purpose of random assignment?
a. The observational units in this study are the individual Mung bean plants that were grown in pots with either biochar-containing soil or soil without biochar.b. The variables in this data set are: - Treatment variable: whether the pot contained soil with biochar or without biochar (categorical) - Grain yield variable: the amount of grain produced by each Mung bean plant (quantitative)c. In this study, the treatment variable (presence of biochar in soil) would be the explanatory variable, as researchers are interested in how this factor affects the grain yield of Mung bean plants. The grain yield variable would be the response variable, as it is the outcome being measured.d. A given value in this study would be a statistic if it describes a sample (e.g., average grain yield of the 100 Mung bean plants in the study) and a parameter if it describes a population (e.g., average grain yield of all Mung bean plants in the region). The appropriate notation for a statistic is typically a lowercase letter (e.g., x̄ for sample mean) and for a parameter is typically a Greek letter (e.g., μ for population mean).e. The summary statistics given in the problem would likely include measures such as the mean grain yield, standard deviation of grain yield, and possibly the proportion of plants with biochar-containing soil. These statistics help summarize the data and provide insights into the relationship between biochar use and grain yield.f. The target population in this study would be all Mung bean plants grown in the region where the study was conducted.g. In this study, selection bias may be present if the coin flip method used to assign biochar-containing soil was not truly random. This could potentially introduce bias into the results. Non-response bias would not be relevant in this study, as all plants were measured. Response bias could be a concern if the researchers' measurement of grain yield was inaccurate or inconsistent.h. Types of graphs that could be used to plot the variables in this study include: - Bar graph or pie chart for the treatment variable (presence of biochar) - Histogram or box plot for the grain yield variablei. The treatment variable (presence of biochar) would be plotted in a bar graph or pie chart, while the grain yield variable would be plotted in a histogram or box plot.j. The study design in this case is a randomized experiment, as the researchers used a coin flip to randomly assign the treatment (biochar or no biochar) to each pot. This allows for causal inferences to be made about the relationship between biochar use and grain yield.k. A potential confounding variable in this study could be the amount of sunlight each plant received, as this could impact both the growth of the plant and the grain yield. To determine if sunlight is a confounding variable, researchers could plot grain yield against sunlight exposure and see if there is a relationship.l. The scope of inference in this study would be limited to the population of Mung bean plants in the region where the study was conducted. i. We can determine a causal relationship between the use of biochar in soil and the grain yield of Mung bean plants because the study design was a randomized experiment. ii. The results from this study can be generalized to the population of Mung bean plants in the region where the study was conducted, but may not be applicable to Mung bean plants in other regions.m. The purpose of random sampling is to ensure that the sample is representative of the population and to reduce the risk of bias in the selection of observational units.n. The purpose of random assignment is to ensure that treatment groups are comparable and any differences in outcomes can be attributed to the treatment being studied rather than other factors.
