It is well documented that when people believe they are receiving a treatment, they experience what they expect will be the effects of that treatment. Placebos help to verify whether an experimental treatment is effective by reducing the likelihood that study participants’ expectations or beliefs about treatments, or about whether they received a treatment, skew study results. 

It is well documented that when people believe they are receiving a treatment, they experience what they expect will be the effects of that treatment.  In a blind study, no participant being studied is aware which group he or she is in, or exactly what treatment he or she received. This can help prevent study participants’ expectations and beliefs about treatments, or about whether they received a treatment, from skewing study results.

When researchers are aware which study participants have received which treatments, they may consciously or subconsciously behave in ways that skew results of the study towards the researchers’ own perspectives or interests. In a double-blind study, during the study neither the researchers nor any participant is aware which group he or she is in, or exactly what treatment he or she received. This can prevent researcher behavior from skewing study results.

The control group in an experiment does not receive the experimental treatment, but resembles the group receiving the experimental treatment. Thus, the dependent variable associated with the control group is not affected by the independent variable in the experiment. This allows the researcher to compare the effect of the experimental treatment on the experimental group with the effect of no treatment, making the effect of the treatment easier to verify.

The experimental group in an experiment receives the experimental treatment. The dependent variable associated with the experimental group is affected by the independent variable in the experiment, while the dependent variable associated with the control group is not. 

A statistically significant result of an experiment is one in which a change in the experimental group’s dependent variable is attributable to a change in the independent variable. In other words, a statistically significant result in a well designed experiment is one that is large enough in scale that it is unlikely to be a result of mere chance. In the table provided, the difference between the total ad clicks resulting from each of the slogan types is minuscule--a difference of only 3 clicks out of over 2,000 for each type. This suggests that the results may simply have been the result of chance, since the difference in total clicks is so small in scale that it is difficult to clearly attribute to the change in slogan types.

Sampling bias occurs when populations are included or excluded from study participation in a way that systematically affects the sample’s representativeness of the population the researcher seeks to gain knowledge about. Given the small population of students at the high school, it is highly unlikely that all mothers in the city are represented in the sample; and given that the high school is both small and private, it is unlikely that the sample is representative of all mothers in the city. Interviewer bias occurs when there is a possibility that an interviewer may behave in ways that consciously or unconsciously influence respondents to give answers skewed towards the interviewer’s perspective or interests. Response bias occurs when respondents consciously or subconsciously give responses they believe the interviewer wants to hear. Interviewer and response bias may result from the fact that the students attend the same schools that the respondents’ children attend, and the fact that the small size of the high school increases the likelihood of personal connections existing between the students and the respondents. The description provides no evidence of measurement bias, or systematic incorrect measurement, in this study.

The key to solving this problem is noticing that there is something special about ; they are all cubes of different values (5, x, 3). Therefore, we can apply the Sum of Cubes formula, which is:

In our case, a=5x and b=3. Plugging this in, we get

Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.

The key to solving this problem is noticing that there is something special about 8, , and 64; they are all cubes of different values (2, a, and 4). Therefore, we can apply the Difference of Cubes formula, which is:

In our case, a=2a and b=4. Plugging this in, we get

Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.

The key to solving this problem is noticing that there is something special about 8, , and 216; they are all cubes of different values (2, x, and 6). Therefore, we can apply the Sum of Cubes formula, which is:

In our case, a=2x and b=6. Plugging this in, we get

Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.