81
Paper 3 – Practical Example
Example
Rodrigo and Thiago are two full-time football players in Spain . They are belonged to two different teams in a football league . As being the main striker of their teams , their numbers of goals are investigated .
Part I – Models for the Population 1
The following table shows the number of goals x scored by Rodrigo in the football league each year , where n is the number of years after 2011 :
n |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
x |
10 |
15 |
20 |
27 |
28 |
24 |
18 |
12 |
( a ) |
The relationship between the variables is modelled by the regression equation |
2 x( n) an bn c � � � .
( 1 ) Write down the values of a , b and c .
( 2 ) Hence , estimate the number of goals scored by Rodrigo in 2020 , giving the answer correct to the nearest integer .
20
( 3 ) Comment the validity of this estimation .
( b ) A hypothesis test is conducted at a 5 % significance level to test the probability of a shoot tried by Rodrigo converted to a goal is greater than 0.6 .
From 2012 to 2019 , Rodrigo has tried 251 shoots in total .
( 1 ) Write down the total number of goals scored by Rodrigo from 2012 to 2019 .
( 2 ) Write down the null hypothesis of the test .
( 3 ) Write down the alternative hypothesis of the test .
( 4 ) Find the p -value .
( 5 ) State the conclusion of the test with a reason .
www . seprodstore . com
305