Your Practice Set – Applications and Interpretation for IBDP Mathematics
2 . Two surveys are conducted to measure the students ’ satisfaction on the services provided by the sports centre . A score from 0 to 10 is used in the surveys , where 0 represents absolute dissatisfaction and 10 represents absolute satisfaction . The table below shows the results of the surveys completed by 8 students :
Student |
A |
B |
C |
D |
E |
F |
G |
H |
Scores from the first survey ( x ) |
8 |
10 |
8 |
9 |
10 |
6 |
3 |
3 |
Scores from the second survey ( y ) |
6 |
10 |
7 |
5 |
9 |
6 |
5 |
3 |
The student union committee members want to investigate whether the mean scores of the second survey is lower . A paired t -test is conducted at a 5 % significance level . Define d �x � y .
( a ) |
Write down the alternative hypothesis of the test . |
( b ) |
Find the p -value. |
( c ) |
Write down the value of t , the test statistic . |
( d ) |
State the conclusion of the test with a reason . |
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[ 2 ]
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3 . A teacher wants to know whether the supplementary lessons between the mock examination and the official examination can improve students ’ mean score in the official examination . The table below shows the scores ( out of 100 ) of 9 students in two examinations :
Student A B C D E F G H I
Mock exam score ( x ) |
45 |
55 |
83 |
79 |
82 |
62 |
67 |
80 |
75 |
Official exam score ( y ) |
37 |
52 |
61 |
90 |
94 |
96 |
87 |
71 |
81 |
An appropriate test is conducted at a 10 % significance level .
( a ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( b ) Find the p -value .
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