Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 76
1 . The amount of chemical in a substance is being studied . It is given that the population standard deviation of the amount of chemical is 3.1 mg . 60 samples of the substances are randomly selected such that the sample mean of the amount of chemical is 16.2 mg . A hypothesis test is conducted at a 5 % significance level to test whether the population mean � differs from 17 mg .
( 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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2 . The numbers of chocolate balls in gift boxes is being studied . It is given that the population variance of the number of chocolate balls is 4 . Eighty gift boxes are randomly selected to form a sample such that the sample mean number of chocolate balls in each box is 27.95 . Gordon claims that the population mean number of chocolate balls � is less than 28 .
A hypothesis test is conducted at a 10 % significance level to test Gordon ’ s claim .
( 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 .
[ 2 ]
[ 2 ]
[ 2 ]
3 . The scores of a survey about the performance of a singer is being studied . It is given that the population variance of the scores is 3 . 16 surveys are randomly selected to form a sample , as shown as follows :
7 9 8 5 3 6 10 10 10 8 7 10 4 9 7 2
A hypothesis test is conducted at a 5 % significance level to test whether the population mean score � is greater than 7 .
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