13 . Two surveys are conducted to measure the residents ’ satisfaction on the services provided by the community 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 6 residents :
Resident |
A |
B |
C |
D |
E |
F |
Scores from the first survey ( x ) |
5 |
7 |
3 |
6 |
8 |
8 |
Scores from the second survey ( y ) |
4 |
9 |
5 |
5 |
9 |
9 |
The manager of the community centre wants to investigate whether the mean scores of the second survey has improved . A paired t -test is conducted at a 5 % significance level . Define d �x � y .
( 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 .
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