( c ) Write down the unbiased estimates for the population
A
( i ) mean ;
( ii ) standard deviation ;
( iii ) variance .
2
� goodness of fit test is conducted at a 5 % significance level to determine whether the examination score can be modelled by a normal distribution with parameters values evaluated in ( c ).
( d ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down f .
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( iii ) Hence , write down the degree of freedom of the test .
( iv ) Find the p -value .
( v ) Hence , state the conclusion of the test with a reason .
[ 7 ] The organizer starts an online system such that students who are interested in participating in the mock examination in the following month can reserve the quota . The number of students , X , reserving the quota follows a Poisson distribution with parameter � per hour .
A hypothesis test is conducted at a particular significance level to test whether
� is less than 11 .
( e ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
The null hypothesis is rejected if it is observed that at most five students reserving the quotas in a particular hour .
( f ) Find the probability that a Type I error is made .
The actually value of � is 7 .
( g ) Find the probability that a Type II error is made .
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