Answer
The p-value is obtained as 0.1719.
Work Step by Step
The p-value approach is used to determine whether the null hypothesis can be rejected by using the binomial probability formula.
The binomial probability formula is defined as
\[P\left( X=k \right)={}^{n}{{C}_{k}}\times {{p}^{k}}\times {{\left( 1-p \right)}^{n-k}}\]
Here,\[p=\frac{1}{2}\]for a median test, \[X=k\] is the number of positive and negative signs, and n is the total number of plus and minus signs.
The provided data shows that there are 3 observations above the median difference value of zero and 7 observations below the median difference value of zero. Therefore, there are 7 minus signs and 3 plus signs. Also, n is obtained as:
\[\begin{align}
& n=7+3 \\
& =10
\end{align}\]
Since\[n=10<25\], this is a small-sample case and a two-tailed test. The test statistic,k, is the smaller of the number of negativeand positive signs for a two-tailed test.
Therefore, the test statistic is \[k=3\]. See p-value calculations given above.
