The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...

Metal ions can be separated from one another by complexation with organic ligands–the chelating agent– to form uncharged chelates. Here, the chelating agent must contain hydrophobic groups and behave as a weak acid, losing a proton to bind with the metal. Since most organic ligands used in this process are insoluble or undergo oxidation in the aqueous phase, the chelating agent is initially added to the organic phase and extracted into the aqueous phase. The metal-ligand complex is formed in...

Kirchhoff's rules quantify the current flowing through a circuit and the voltage variations around the loop in a circuit. Applying Kirchhoff's rules generates a set of linear equations that allow us to find the unknown values in circuits. These may be currents, voltages, or resistances.
When applying Kirchhoff's first rule, the junction rule, label the current in each branch and decide its direction. If the chosen direction is wrong, it will have the correct magnitude, although the current will...

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...

An experimental design is a systematic process that allows researchers to evaluate the relationship between dependent and independent variables. There are three widely used types of experimental design - pre-experimental design, true experimental design, and quasi-experimental design. In pre-experimental design, the researcher compares the data before and after some interventions or treatments. The true-experimental design has more than one purposefully created group, a commonly measured...

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. However, sometimes, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000...