Problem

A cafe owner wishes to know whether the price of strawberry jam is related to the taste of the jam. He finds a website that lists the price per 100 grams and a mark for the taste, out of 100, awarded by a judge, for 9 different strawberry jams A, B, C, D, E, F, G, H and I. He then ranks the marks for taste and the prices.

The ranks are shown in the table below.

Rank	1	2	3	4	5	6	7	8	9
Price	A	B	E	C	D	F	G	H	I
Taste	A	B	F	E	H	G	I	C	D

(a) Calculate Spearman’s rank correlation coefficient for these data.

(b) Test, at the 5% level of significance, whether or not there is a relationship between the price and the taste of these strawberry jams. State your hypotheses clearly.

A friend suggests that it would be better to use the price per 100 grams, $c$, and the mark for the taste, $m$, for each strawberry jam rather than rank them.

Given that

$$S_{cc}=2.0455 \qquad S_{mm}=243.5556 \qquad S_{cm}=16.4943$$

(c) calculate the product moment correlation coefficient between the price and the mark for taste of these strawberry jams, giving your answer correct to 3 decimal places.

(d) Use your value of the product moment correlation coefficient to test, at the 5% level of significance, whether or not there is evidence of a positive correlation between the price and the mark for taste of these 9 strawberry jams. State your hypotheses clearly.

(e) State which of the tests in parts (b) and (d) is more appropriate for the cafe owner to use. Give a reason for your answer.