Data Modeling Examples and Frequently Asked Questions

The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions. 
$\begin{array}{|cccc|}\hline \text{Treatment}& \text{Number of Observations}& \text{Sample Mean}& \text{Sum of Squares (SS)}\\ \text{Private prep class}& 60& 680& 265,500.00\\ \text{High school prep class}& 60& 650& 276,120.00\\ \text{No prep class}& 60& 635& 302,670.00\\ \hline\end{array}$ 
Using the data provided, complete the partial ANOVA summary table that follows (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations G, the grand total, can be calculated from the values of T once you have calculated them.) 
$\begin{array}{|cccc|}\hline \text{Source}& \text{Sum of Squares (SS)}& df& \text{Mean Square (MS)}\\ \text{Between treatments}& & & \\ \text{Within treatments}& & & \\ \hline\end{array}$ 
ANOVA summary tables typically have a "Total" row not induded in the partial table you just completed. Which of the following is a possible reason for induding this row? 
a) The ${\displaystyle M{S}_{\to tal}}$ is used in the calculation of the F test statistic. 
b) The ${\displaystyle S{S}_{\to tal}}$ is used in the calculation of the F test statistic. 
c) The total sums of squares is the sometimes called the "error term" 
d) The $S{S}_{total}$ is sometimes easier to calculate than. $S{S}_{between}$ Since $S{S}_{within}+S{S}_{between}=S{S}_{total}$, you can use $S{S}_{total}$ to calculate $S{S}_{between}$.
In ANOVA, the F test statistic is the ? of the between-treatments variance and the within-treatments variance. the value of the F test statistic is ? 
When the null hypothesis is true, the F test statistic is ? When the null hypotesis is false, the F test statistic is most likely ? In general, you should reject the null hypotesis for.

Of the following, which is untrue?
A.Majority of Z scores in a right skewed distribution are negative. 
B.In skewed distributions the Z score of the mean might be different than 0. 
C.For a normal distribution, IQR is less than ${\displaystyle 2\times SD}$. 
D.Z scores are helpful for determining how unusual a data point is compared to the rest of the data in the distribution.

Presenting data in the form of table. For the data set shown by the table, Solve,
a) Create a scatter plot for the data.
b) Use the scatter plot to determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data. (If applicable, you will use your graphing utility to obtain these functions.)
$\begin{array}{|cc|}\hline \text{Intensity (wattd per}mete{r}^2)& \text{Loudness Level (decibels)}\\ 0.1\text{(loud thunder)}& 110\\ 1\text{(rock concert, 2 yd from speakers)}& 120\\ 10\text{(jackhammer)}& 130\\ 100\text{(jet take off, 40 yd away)}& 140\\ \hline\end{array}$

MODELING REAL LIFE. To make 18 glasses of juice, combine 0.25 cups of juice concentrate with 2 cups of water. Use how much juice concentrate? How much water do you use? You use ___ cups of juice concentrate and ___ cups of water.