c. (6 pts) Using the qualitative variable (the fourth variable), create a qualitative frequency distribution showing both frequencies and relative frequencies.

4. Graphs and Their Analysis

a. (6 pts) Construct a qualitative bar chart from the frequency distribution from 3c. 

b. (2 pts) Answer the following questions about the qualitative bar chart in paragraph form.

• How many bars are there?

• Which bar has the highest frequency?

• Which bar has the lowest frequency?

c. (18 pts) For each quantitative variable, create a histogram with four to six classes.

d. (6 pts) For each histogram, answer the following questions in paragraph form.

• What are the largest and smallest data values?

• Is it symmetric, skewed to the left, or skewed to the right?

• How many peaks does it have, and where are they located?

• Does it have any gaps and, if so, where are they?

• Does it have any extreme values and, if so, what are they?

e. (8 pts) For the two comparable quantitative variables (the first 2 variables), create side-by-side horizontal box plots. 

f. (4 pts) Answer the following questions about the side-by-side box plots.

• Which plot has the largest value?

• Which plot has the smallest value?

• Which plot has the largest median?

• Which plot is more skewed?

• Which plot has the largest range?

• Which plot has the largest interquartile range?

g. (4 pts) Create a single horizontal box plot of the third quantitative variable. 

h. (2 pts) Answer the following questions about the single box plot.

• Are there any outliers?

• What is the median value?

• Is the box plot skewed left, skewed right or symmetric?

i. (12 pts) Using the first and third variable, create a scatter diagram with the regression line.

j. (8 pts) Referring to the scatter diagram you just made, do the following.

• Decide whether the association between the two variables is strong, moderate or weak, and also whether the association is positive, negative or neither.

• Identify any outliers or influential observations on the scatter diagram.

• Find and state the equation of the regression line in the scatter diagram.

• Find the coefficient of determination and then interpret the coefficient of determination in the context of the scatter diagram you just created.

5. Hypothesis Tests: For each of the following hypothesis tests, i) name the test you ran, ii) state the test statistic, iii) state the P-value, and iv) state your conclusion to the test in English

a. (10 pts) Run a chi-square goodness of fit test at 95% confidence to see whether or not the outcomes of your qualitative variable are equally likely. 

b. (10 pts) Run a dependent difference test to see if the means of variables 1 and 2 are equal at 95% confidence.

c. (10 pts) Test to see if there is significant linear correlation between variables 1 and 3 at 95% confidence.

d. (12 pts) Run the Shapiro-Wilk test at 95% confidence for each of the quantitative variables (variables 1 through 3) to see if these variables are normally distributed.  When finished with this step, you will have run three different tests.

6. Table of Data: (4 points)  Insert a table showing all your data at the end of the project.