  A set family ${\cal F}$ is called intersecting if every two members of ${\cal
F}$ intersect, and it is called uniform if all members of ${\cal F}$ share a
common size. A uniform family ${\cal F} \subseteq \binom{[n]}{k}$ of
$k$-subsets of $[n]$ is $\varepsilon$-far from intersecting if one has to
remove more than $\varepsilon \cdot \binom{n}{k}$ of the sets of ${\cal F}$ to
make it intersecting. We study the property testing problem that given query
access to a uniform family ${\cal F} \subseteq \binom{[n]}{k}$, asks to
distinguish between the case that ${\cal F}$ is intersecting and the case that
it is $\varepsilon$-far from intersecting. We prove that for every fixed
integer $r$, the problem admits a non-adaptive two-sided error tester with
query complexity $O(\frac{\ln n}{\varepsilon})$ for $\varepsilon \geq \Omega(
(\frac{k}{n})^r)$ and a non-adaptive one-sided error tester with query
complexity $O(\frac{\ln k}{\varepsilon})$ for $\varepsilon \geq \Omega(
(\frac{k^2}{n})^r)$. The query complexities are optimal up to the logarithmic
terms. For $\varepsilon \geq \Omega( (\frac{k^2}{n})^2)$, we further provide a
non-adaptive one-sided error tester with optimal query complexity of
$O(\frac{1}{\varepsilon})$. Our findings show that the query complexity of the
problem behaves differently from that of testing intersectingness of
non-uniform families, studied recently by Chen, De, Li, Nadimpalli, and
Servedio (ITCS, 2024).
