2 . In a library , the habit of reading books of young people is investigated . The table below shows the number of fiction books read by two different groups of people in a particular month , after they have filled in a survey :
The group of 10-year-old students The group of 20-year-old people
3 4 7 6 9 11 3 1 4 6
4 6 5 4 0 1 0 3 2
The library manager wants to investigate whether 10-year-old students read more than 20-year-old people on average . Let �
1 and �
2 be the mean number of fiction books read by the 10-year-old students and the 20-year-old people respectively . A t -test is conducted at a 5 % significance level , and it is assumed that the variances of the number of fiction books read by two different groups of people are the same .
( a ) |
Write down the alternative hypothesis of the test . |
( b ) |
Find the p -value. |
( c ) |
State the conclusion of the test with a reason . |
One person from each age group above is randomly selected . |
[ 1 ]
[ 2 ]
[ 2 ]
( d ) |
( i ) |
Find the probability that both of them read at least five fiction |
|
|
books . |
( ii ) Find the probability that at least one of them read at least five fiction books .
The library manager also wants to investigate the relationship between the ages and the reading preferences of 120 library users from another three different age groups . A survey had been conducted and the following table shows the results :
[ 4 ]
Age
Reading preference |
Fiction Novel Newspaper |
30-year-old |
11 |
25 |
4 |
40-year-old |
16 |
16 |
8 |
50-year-old |
5 |
3 |
32 |
A
2
� test for independence is conducted at a 1 % significance level .
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