Apps. and Interpretation for IBDP Maths Ebook 2 | Page 323

Part III – Combining the Two Populations

An investor is going to investigate the data of the numbers of books sold by Nina and Olga , summarized as follows :

n 1 2 3 4 5 7 9

The investor would like to perform a suitable statistical test at a 10 % significance level to determine whether on average Olga can sell more books than Nina each year .

( e ) ( 1 ) Write down the null hypothesis of the test .

( 2 ) Write down the alternative hypothesis of the test .

( 3 ) Find the p -value .

( 4 ) State the conclusion of the test with a reason .

The product moment correlation coefficient of the numbers of books sold by the two authors is � . The investor would also like to perform a hypothesis test at a 5 % significance level to test whether there is any correlation between the two variables .

( f ) ( 1 ) State an assumption for testing � .

( 2 ) Write down the null hypothesis of the test .

( 3 ) Write down the alternative hypothesis of the test .

( 4 ) Find the p -value .

( 5 ) State the conclusion of the test with a reason .

Let d � y � x . The following table shows the distribution of d :

n 1 2 3 4 5 7 9

d � 10 6 16 25 20 � 8 19

( g ) ( 1 ) Construct a 90 % confidence interval for the population mean of d .

( 2 ) Is the above result consistent with the conclusion of the hypothesis test in ( e )? Explain your answer .

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