Question

Step 2: In the question above, find the test statistic z (using the method of your choice--graphing calculator, Excel, app, formula), to at least two places after the decimal point.

Answer 1

The formula for the statistical z-score is :

`z=\frac{\mu_1-\mu_2}{\sqrt[]{(\sigma^2_1)/(n_1)+(\sigma^2_2)/(n_2)}}`

Where n1 and n2 are the sample sizes

u1 and u2 are the sample means

and

o1 and o2 are the standard deviation

From the given problem, we have :

u1 = 3.16

u2 = 3.28

n1 = 103

n2 = 225

o1 = 0.52

o2 = 0.46

Substitute the values to the formula :

`\begin{gathered} z=\frac{3.16-3.28}{\sqrt[]{(0.52^2)/(103)+(0.46^2)/(225)}}=(-0.12)/(0.0597) \\ z=-2.01 \end{gathered}`

Therefore, the answer is z = -2.01