19 students were asked to perform a reflex test catching a falling ruler. Their performance was measured by how high on the ruler they caught it. A Mann-Whitney U test was conducted to determine if there was a difference in catching speed between students who do sport and those who don't. The null hypothesis was that the two student groups come from identical populations. The alternative hypothesis was that the groups would differ in catching speed. Test statistics and rankings were calculated for the two groups. Based on the critical value from tables, the null hypothesis was rejected, indicating the students who do sport caught the ruler faster.

2.  The samples didn’t come from identical
populations or the samples came from
different populations.
 It’s a random sample.

3. 19 students were asked to do a reflex test
where they had to drop a ruler and see how
fast they could catch it. It was measured by
how far up the ruler (in cm) they caught it.
Carry out a Mann-Whitney U test, at the 5%
level of significance, to investigate whether
on average there is a difference between the
speed in which students that do and don’t do
sport catch the ruler.

4.  H₀: The two samples come from identical
populations.
 H₁: The two samples don’t come from
identical populations, there will be a
difference in how fast the ruler is caught on
average between the students that do sport
and those that don’t.
For the alternate hypothesis you need to
include something that fits in with the
context of the question.

5.  The data needs to be ranked as a whole, with
the rankings under whichever category it fits
under.
 Rank the data in ascending order and make
sure you can distinguish between the data
belonging to the different lists.

6. Sport No sport
Cm Ranking Cm Ranking
2
3
6
7.5
7.5
9
1
2
5.5
8.5
8.5
11.5
4
4.5
6
7
8
9
11
12
13
13.5
14
16
16
3
4
5.5
7
10
11.5
13
14
15
16
17
18.5
18.5
37 153

7.  U = T – ½ n(n+1)
 37 – ½ x 6 x (6+1) = 16 <- test statistic
 153 – ½ x 13 x (13+1) = 62
It’s a good idea to check that the numbers add
up properly.
 Un+Um or mxn
 16 + 62 = 78
 13 x 6 = 78

8.  Find the critical value on the table
The critical value differs based on if it’s two
tailed or one tailed and the level of
significance.

9.  Because 16 ≤ 16 we reject the H₀, so there is
sufficient evidence to suggest that the
students that do sport catch the rulers faster
than the students that don’t do sport.
The conclusion always needs to be put in
context.