(Solved): Suppose that George wants to determine if the number of insects in a given area is related to the ...

Suppose that George wants to determine if the number of insects in a given area is related to the number of flowers in that area. He creates three $$1{\mathrm{m}}^2$$ quadrats in his backyard and counts the number of flowers $$(x)$$ and number of insects $$(y)$$ in each quadrat. His data are shown in the table. Calculate the Pearson product-moment correlation coefficient, $$r$$, using the formula $$r=\frac{?z_{xi}?z_{yi}}{n?1}$$ where $$z$$ is the $$z$$-score for each value, $$x_i$$ represents the $$x$$-value for each data point, $$y_i$$ represents the $$y$$-value for each data point, and $$n$$ represents the sample size. Complete the following five steps to calculate $$r$$, and give each of your answers precise to two decimal places. Step 1. Calculate the $$z$$-score for each $$x$$-value. $$z_{x1}=\frac{x_1?\stackrel{?}{x}}{s{d}_x}=z_{x2}=\frac{x_2?\stackrel{?}{x}}{s{d}_x}=\left[z_{\text{Incorrect }}\right]z_{x3}=\frac{x_3?\stackrel{?}{x}}{s{d}_x}=[\underset{\text{Incorrect }}{\underbrace{[}}]$$ Step 2. Calculate the $$z$$-score for each $$y$$-value. $$z_{y1}=\frac{y_1?\stackrel{?}{y}}{s{d}_y}=\left[z_{\text{Incorrect }}\right]z_{y2}=\frac{y{y}_2?\stackrel{?}{y}}{s{d}_y}=z_y=\frac{y_3?\stackrel{?}{y}}{s{d}_y}=$$ Step 3. For each data point, calculate the product of the pair of $$z$$-scores. Step 4. Sum the products of each pair of z-scores. $$?\left(z_{xi}?z_{yi}\right)=\underset{\text{Insorrect }}{\underbrace{[}}]$$ Step 5. Calculate the correlation coefficient. $$r=\frac{?\left(z_{xi}?z_{yd}\right)}{n?1}=$$ Incorrect