Question

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

Answer 1

The given information is:

n=8

u=21.1

sd=14.9

`\begin{gathered} H_0\colon\mu_d=0 \\ H_1\colon\mu_d>0 \end{gathered}`

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:

`Z=\frac{\bar{x}-\mu_0}{\sigma/\sqrt[]{n}}`

By replacing the known values we obtain:

`\begin{gathered} Z=\frac{21.1-0}{14.9/\sqrt[]{8}} \\ Z=4.005 \end{gathered}`

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:

`p=0.000031\approx0.0000`

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.