On the same day , in order to find the value of � , Rachel also practiced 100 metres run for five times , and the times used are recorded as follows :
13.9 s , 14.7 s , 13.5 s , 14.0 s , 14.2 s
( e ) Find the unbiased estimates for
( i ) � ;
( ii ) � . [ 4 ]
( f ) Construct a 95 % confidence interval for � , giving the answer to three decimal places .
In February 2021 , the manager of the running club investigates the best records for six athletes in the club to finish 100 metres runs in January and February :
Athlete |
Patty |
Quinn |
Rachel |
Sally |
Tina |
Ursula |
|
Best record in
January 2021 ( j s
)
|
13.2 s |
13.8 s |
13.5 s |
15.0 s |
14.0 s |
13.0 s |
Best record in February 2021 ( f s )
13.1s 14.2 s 13.4 s 14.8 s 14.9 s 13.0 s
[ 2 ]
The manager wants to investigate whether on average the athletes show improvement in February . A paired t -test is conducted at a 5 % significance level . Define d � j � f .
( g ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( iii ) Find the p -value .
( iv ) Write down the value of t , the test statistic .
( v ) State the conclusion of the test with a reason . [ 7 ]
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