2 . This question aims at investigating the results of a Mathematics mock examination .
Three hundred students attended a Mathematics mock examination . The following table shows the distribution of their final grades , where 1 represents the lowest grade and 7 represents the highest grade .
Grade 1 2 3 4 5 6 7 Frequency 12 27 58 103 45 35 20
The grades of two students are randomly selected .
( a ) ( i ) Find the probability that both grades are either 5 , 6 or 7 .
( ii ) Given that the probability that both grades are either 5 , 6 or 7 , find the probability that both grades are the same .
[ 5 ]
The organizer of the mock examination claims that 18 % of the students attending the mock examination takes the Mathematics Higher level course . A sample of 25 students are interviewed , and 7 of them takes the Mathematics Higher level course .
A hypothesis test is conducted at a 5 % significance level to test whether there are actually more than 18 % of the students attending the mock examination takes the Mathematics Higher level course .
( b ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( iii ) Find the p -value .
( iv ) Hence , state the conclusion of the test with a reason .
The following table shows the distribution of the actual scores :
[ 6 ]
Score ( x ) |
0
� x
�
20
|
20
� x
�
40
|
40
� x
�
60
|
60
� x
�
80
|
80
� x
�100
|
|
Observed
Frequency
|
20 |
72 |
140 |
45 |
23 |
|
Expected
Frequency
|
21.7 |
77.4 |
116.7 |
84.2
� f
|
f |
© SE Production Limited 8 All Rights Reserved 2021