2.3 percent of individuals fall two standard deviations above the mean in a normal distribution. 2.3% of 1000 individuals is 23 individuals that fall above this cutoff. 

Convert the percentage into a ratio.

Create a ratio using the total number of the sample size. Use the variable  as a representation of the number of individuals that fall two standard deviations above the mean.

Create a proportion using the two ratios.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

Any correlation between .30 and .69 is considered moderate in strength. Anything above .60 is considered strong. Anything below .30 is considered weak or no correlation.  

A type I error occurs when a null hypothesis is rejected when researchers should have failed to reject the null hypothesis, in other words, when the researchers reject a true hypothesis. Remember, a null hypothesis is the assumption that there is no difference between the groups participating in the study. So if a type I error occurs, that means that the researchers are stating there is a difference between the groups when there really is not a difference. A Type II error involves the acceptance of a false hypothesis.

A type II error occurs when researchers fail to reject their null hypothesis when they should have rejected it. A null hypothesis is the assumption that there is no difference between the groups being studied. So if a type II error occurs, that means that the researchers are stating there is not a difference between the groups when there really is one.

Central tendency measures include the mean, median, and mode. In this case, the median would be best because several outliers skew this data set (e.g. perfect scores). The mean would be influenced strongly by these outliers. 

A correlation coefficient is a measure of the relationship between two variables. Correlation coefficients range from -1 to +1. For this reason -1.5 is incorrect because it is not possible to have a correlation coefficient less than -1. This question is asking for a coefficient with a strong inverse relationship. A positive number indicates a direct relationship, while a negative number indicates an indirect or inverse relationship. The specific number indicates the strength of the relationship. If the correlation coefficient is closer to -1 or +1, then it is said to be strong. As the number moves closer to zero, the strength of the relationship decreases; therefore, -0.90 is the best answer. 

In order to calculate the mean (also called arithmetic average) we need to add all the values together and divide by the number of values. In this case, the total sum is 87 and the number of values is 12, so we perform the following calculation to obtain our mean:

To find the median, we simply arrange the values in order from least to greatest and identify the middlemost number. However, since 12 is an even number, there will not be one single middle value– therefore, we find the average of the two middlemost values. Arranged in ascending order, the data set is:

The 6th and 7th values are 6 and 7, so we know our median is the average of 6 and 7.

The mode is the value that occurs most frequently in the data set. Here, 6 occurs three times and no other number occurs more than twice, which means 6 is our mode.

The "dependent variable" is indicative of the outcome of an experiment, and is recorded as evidence to attempt to provide support for or against a thesis. The independent variable is indeed measured; however,its quantities are irrelevant to an experiment. Control and random variables are not recorded and are only useful when considering the changes to dependent variable. 

A correlation coefficient is a statistical measure of the extent to which two factors vary together. Specifically, it measures how well one factor predicts another on a scale of -1 to 1, with numbers closer to -1 and 1 indicating the strongest relationships. Whether a correlation coefficient is negative or positive does not indicate the strength of the relationship, it simply tells us the direction of the relationship!

Statistical significance is a statistical criterion for rejecting the assumption of no difference between groups in a particular study. In order to establish statistical significance, researchers typically look for a p value of less than .05, which indicates that the study's findings were not obtained due to chance or error.