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Paper 2 – Population Correlation Coefficient
Example
The following table shows the repair cost ($ y ) of a type of machine of a particular age ( x years ) .
Age ( x years ) |
3 |
5 |
7 |
10 |
12 |
Repair cost ($ y ) |
500 |
750 |
800 |
1200 |
1800 |
It is assumed that the two variables follow a bivariate normal distribution with product moment correlation coefficient � . A hypothesis test is conducted at a 5 % significance level to test whether there is a positive 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 .
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( d ) ( i ) Write down the value of a and of b .
( ii ) Explain what the gradient a represents .
( e ) Use the model to estimate the repair cost of a machine with age 9 years .
( f ) ( i ) Write down the correlation coefficient .
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( ii ) Write down the coefficient of determination .
( iii ) Hence , interpret the coefficient of determination . [ 3 ] www . seprodstore . com
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