Your Practice Set – Applications and Interpretation for IBDP Mathematics
2 . The random variable X follows a Binomial distribution with parameters 50 and q , representing the number of trials in an experiment and the probability of success of an event respectively .
A hypothesis test is conducted at a particular significance level to test whether q is greater than 0.92 .
( a ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
[ 2 ] The null hypothesis is rejected if it is observed that at least 49 successes are observed out of 50 trials .
( b ) Find the probability that a Type I error is made .
The actually value of q is 0.94 .
[ 2 ]
( c ) Find the probability that a Type II error is made .
Another random variable Y follows a Poisson distribution with parameter � , representing the rate of occurrences of an event per day .
[ 2 ]
A hypothesis test is conducted at a 5 % significance level to test whether � is greater than 3 . It is observed that 5 occurrences of the event is observed in a particular day .
( d ) Write down the critical region for testing � , giving the answer in the form Y � a. [ 2 ]
( e ) Find the p -value.
( f ) State the conclusion of the test with a reason .
[ 2 ]
[ 2 ]
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