Apps. and Interpretation for IBDP Maths Ebook 1 | Page 365

4. Robert is a football player who is attending a training session to practice his free kick
skills since 2018. His coach is investigating whether the ball speed for Robert’s free kick
is increased in 2019. The tables below show the ball speeds (kilometre per hour) of some
of his free kicks in 2018 and 2019:
Ball speed in 2018 88 85 74 99 101 95 65 108 90
Ball speed in 2019 103 88 94 97 105 132 127 79
Let �
R1
and �
R2
be the mean ball speed of Robert’s free kicks in 2018 and in 2019
respectively. The first t -test is conducted at a 10% significance level to test whether the
mean ball speed for Robert’s free kick has increased, and it is assumed that the variances
of the ball speeds for Robert’s free kick in both years are the same.
(a)
(b)
(c)
State an assumption of conducting the t -test.
Write down the alternative hypothesis of this test.
Find the p -value.
[2]
(d) Write down the value of t , the t -statistic.
[1]
(e) State the conclusion of the test with a reason.
[2]
Marcel is Robert’s friend who also attends the same free kick training program in 2019.
Let �
M 2
be the mean ball speed of Marcel’s free kicks in 2019. The second t -test is
conducted at a 10% significance level to test whether the mean ball speeds of their free
kicks in 2019 are different. The tables below show the ball speeds (kilometre per hour) of
some of Marcel’s free kicks in 2019:
[1]
[1]
Ball speed in 2019 112 85 84 87 95 123 91 101 88
(f) (i) Write down the alternative hypothesis of this test.
23
(ii)
Using the p -value approach to state the conclusion.
[4]
For the above ball speeds of free kicks in 2019, one record from each player is randomly
selected.
(g)
Find the probability that both of them are greater than 110 km/h or both of them
are less than 90 km/h.
[3]
www.seprodstore.com
355