The given information is:
n=8
u=21.1
sd=14.9
[tex]\begin{gathered} H_0\colon\mu_d=0 \\ H_1\colon\mu_d>0 \end{gathered}[/tex]
As we are looking for values "greater than", this is a one-tailed test.
To find the test statistic for this sample let's use the next formula:
[tex]Z=\frac{\bar{x}-\mu_0}{\sigma/\sqrt[]{n}}[/tex]
By replacing the known values we obtain:
[tex]\begin{gathered} Z=\frac{21.1-0}{14.9/\sqrt[]{8}} \\ Z=4.005 \end{gathered}[/tex]
Then, the test statistic for this sample is 4.005.
To find the p-value we need to find P(Z>4.005), then 1-P(Z<=4.005), then looing in a z-score table it is equal to:
[tex]p=0.000031\approx0.0000[/tex]
Then, the p-value is less than or equal to the significance level of 0.05, then we should reject the null hypothesis and accept the alternate hypothesis Ha.
