TEST STATISTIC
The formula used to calculate the test statistic is given to be:
[tex]z=\frac{\bar{x}_1-\bar{x}_2}{\sqrt[]{\frac{SD^2_1}{n_1}+\frac{SD^2_2}{n_2}}}[/tex]
The following parameters are provided in the question:
[tex]\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}[/tex]
Substituting these values, we can calculate the test statistic to be:
[tex]\begin{gathered} z=\frac{75.4-83.3}{\sqrt[]{\frac{9.7^2}{12}+\frac{17.8^2}{19}}} \\ z=-1.595 \end{gathered}[/tex]
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:
[tex]p-value=0.0554[/tex]
The significance level, α, is 0.02.
Therefore, the p-value is greater than α.
Thus, we do not reject the hypothesis.
