Part III – Combining the Two Populations
Sergio , a football data analyst , is going to investigate the combined data of Rodrigo and Thiago , summarized as follows :
n 1 2 3 4 5 6 7 8
x |
10 |
15 |
20 |
27 |
28 |
24 |
18 |
12 |
y |
12 |
8 |
7 |
18 |
23 |
26 |
22 |
17 |
Sergio would like to perform a paired t -test at a 5 % significance level to determine whether on average Rodrigo scores more goals than Thiago each year .
( e ) ( 1 ) Write down the null hypothesis of the test .
( 2 ) Write down the alternative hypothesis of the test .
( 3 ) Find the p -value .
( 4 ) Write down the value of t , the t -statistic .
( 5 ) State the conclusion of the test with a reason .
The product moment correlation coefficient of the numbers of goals scored by the two players is � . Sergio would also like to perform a hypothesis test at a 10 % significance level to test whether there is a positive correlation between the two variables .
( f ) ( 1 ) State an assumption for testing � .
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( 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 .
Let s �x � y be the sum of the number of goals scored by Rodrigo and Thiago in each year . Let sn ( ) be the cubic regression equation used to model the relationship between
n and s .
( g ) ( 1 ) Write down the equation of sn ( ), giving the coefficients correct to 6 significant figures if necessary .
( 2 ) Is it true that s( n) �x( n) � y( n) ? Explain your answer .
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