Your Practice Set – Applications and Interpretation for IBDP Mathematics
2 . The following table shows the number of webpages y visited by a student who spend
x minutes to access the internet .
Time ( x minutes ) |
5 |
10 |
15 |
20 |
25 |
30 |
Number of webpages ( y ) |
4 |
3 |
1 |
16 |
21 |
23 |
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 any 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 .
[ 2 ]
[ 2 ]
[ 2 ]
( d ) ( i ) Write down the value of a and of b .
( ii ) Explain what the gradient a represents . [ 3 ]
( e ) Use the model to estimate the number of webpages visited by a student who spend 22 minutes to access the internet , giving the answer correct to the nearest integer .
[ 2 ]
( f ) ( i ) Write down the correlation coefficient .
( ii ) Write down the coefficient of determination .
( iii ) Hence , interpret the coefficient of determination . [ 3 ]
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