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.

where n equals the number of events.

To answer this question, you must first calculate Willow's total points from the 3 exams. The total points will be equal to 3 times the original average:

95*3=285

Now, if the 90 is removed, his new total will be:

285-90=195

With the score dropped, her new total number of exams is 2. Therefore, the new average is:

This question relates to the 68−95−99.7 rule of normal distribution. We know that 95% of the data are within 2 standard deviations from the mean.

In this case this means that 95% of the students are between

15.5−2⋅0.6 and 15.5+2⋅0.5 

15−1.2 and 15+1.2

13.8 and 16.2

Therefore we have 5% of the students that are outside of this range. Since the normal distribution is symmetric, the proportion of students below 13.8 is the same as the proportion of students above 16.2.

Thus the right answer is one half of 5%, or 2.5%.

2.5% of the students are older than 16.2 years old. 

This question relates to the 68−95−99.7 rule of normal distribution. We know that 95% of the data are within 2 standard deviations from the mean.

In this case this means that 95% of the students are between

23.5−2⋅2.5 and 23.5+2⋅2.5

23.5-5 and 23.5+5

18.5 and 28.5

Therefore we have 5% of the students that are outside of this range. Since the normal distribution is symmetric, the proportion of students below 18.5 is the same as the proportion of students above 28.5.

Thus the right answer is half of 5% or 2.5%.

To begin, we must remember the formula for standard deviation:

where is the standard deviation, N is the number of values in our set,   is the value we're currently evaluating in the summation, and is the mean of our set of numbers. All the summation part of the equation means is that we subtract our mean from each number in the set, square that value, and then add all of those values for each number together. So before we find the values that will be added together, we must first find our mean for the set of numbers:

Now we can determine the value for our summation for each number in the set:

Looking at our equation for standard variation, now all we must do is sum all of the values above, divide by N, and take the square root:

The first step in solving for standrd deviation is to find the mean of the data set.

For this problem:

.

Now we can evaluate the summation:

Now we can rewrite the standard deviation expression:

There are 5 data points, so n = 5