Question

Hi, can you help me answer this question please, thank you!

Answer 1

TEST STATISTIC

The formula used to calculate the test statistic is given to be:

`z=\frac{\bar{x}_1-\bar{x}_2}{\sqrt[]{(SD^2_1)/(n_1)+(SD^2_2)/(n_2)}}`

The following parameters are provided in the question:

`\begin{gathered} \bar{x}_1=75.4 \\ \bar{x}_2=83.3 \\ n_1=12 \\ n_2=19 \\ SD_1=9.7 \\ SD_2=17.8 \end{gathered}`

Substituting these values, we can calculate the test statistic to be:

`\begin{gathered} z=\frac{75.4-83.3}{\sqrt[]{(9.7^2)/(12)+(17.8^2)/(19)}} \\ z=-1.595 \end{gathered}`

Therefore, the test statistic is gotten to be -1.595

P-VALUE

To calculate the p-value, we can use an online distribution calculator. This is shown below:

From the calculator above, the p-value is:

`p-value=0.0554`

The significance level, α, is 0.02.

Therefore, the p-value is greater than α.

Thus, we do not reject the hypothesis.