Your Practice Set – Applications and Interpretation for IBDP Mathematics
4 . The random variable X follows a normal distribution with parameter � , where � represents the mean value of a population . The population variance is 16 .
A hypothesis test is conducted at a particular significance level to test whether � is not equal to 100 .
( 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 the mean of a sample of size 36 is less than 99 or greater than 101 .
( b ) Find the probability that a Type I error is made .
The actually value of � is 101 .
[ 2 ]
( c ) Find the probability that a Type II error is made .
Another random variable Y is normally distributed with parameter � , where � represents the mean value of a new population . The population variance is 20 .
[ 2 ]
A hypothesis test is conducted at a 5 % significance level to test whether � is less than 25 . It is observed that the mean is 20 in a random sample of size 60 .
( d ) Write down the critical region for testing � , giving the answer in the form Y � a. [ 2 ]
( e ) State the conclusion of the test with a reason .
[ 2 ]
Assume that the level of significance is changed to 1 %.
( f ) Write down the new critical region for testing � , giving the answer in the form Y
� a.
[ 2 ]
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