Exercise 80
1 . The following table shows the quiz score ( y marks ) of a student with revision time ( x hours ) .
Revision time ( x hours ) |
2 |
4 |
6 |
8 |
10 |
12 |
Quiz score ( y ) |
90 |
80 |
82 |
60 |
55 |
50 |
It is assumed that the two variables follow a bivariate normal distribution with product moment correlation coefficient � . A hypothesis test is conducted at a 10 % significance level to test whether there is a negative correlation between the two variables .
( a ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( b ) Find the p -value .
( c ) State the conclusion of the test with a reason .
This data can be modelled by the regression line with equation y �ax � b .
( d ) ( i ) Write down the value of a and of b .
[ 2 ]
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( ii ) Explain what the intercept b represents . [ 3 ]
( e ) Use the model to estimate the quiz score of a student who has revised for 7 hours . [ 2 ]
( f ) ( i ) Write down the correlation coefficient .
( ii ) Write down the coefficient of determination .
( iii ) Hence , interpret the coefficient of determination . [ 3 ] www . seprodstore . com
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