Question

d) Every week, Hilda buys four apples and three bananas from her local greengrocer. The table shows the total weight, x grams, of the four apples and the corresponding total weight, y grams, of the three bananas for each of a random sample of 13 weeks.
X 562 633 578 621 558 593 607 638 527 623 579 588 524
Y 366 320 379 407 422 394 325 369 387 395 446 364 457

i). Calculate, to three decimal places, the value of the product moment correlation coefficient, r, between x and y. [3 marks]
ii). Interpret, in context, your value for r . [2 marks]
iii). Howard, Hilda’s husband, claims that each week she buys either big apples and big bananas or small apples and small bananas. Comment on Howard’s claim

Answer 1

Answer to Question #91019 – Math – Statistics and Probability

Question

d) Every week, Hilda buys four apples and three bananas from her local greengrocer. The table shows the total weight, x grams, of the four apples and the corresponding total weight, y grams, of the three bananas for each of a random sample of 13 weeks.

X 562 633 578 621 558 593 607 638 527 623 579 588 524

Y 366 320 379 407 422 394 325 369 387 395 446 364 457

i). Calculate, to three decimal places, the value of the product moment correlation coefficient, r, between x and y. [3 marks]

ii). Interpret, in context, your value for r. [2 marks]

iii). Howard, Hilda’s husband, claims that each week she buys either big apples and big bananas or small apples and small bananas. Comment on Howard’s claim

Solution

Answer to part i).

R=correlation coefficient= $\frac{|n\sum x\times y - (\sum x)\times(\sum y)|}{\left|\sqrt{n\sum x^2 - (\sum x)^2}\right|\times\left|\sqrt{n\sum y^2 - (\sum y)^2}\right|}$

R=correlation coefficient= $\frac{[13\times 2943644 - 7631\times 5031]}{\left|\sqrt{13\times 4496183 - 7631}^2\right|\times\left|\sqrt{13\times 1966807 - 5031}^2\right|}$

R=correlation coefficient= $\frac{-124189}{467.1381\times 507.4741}$

R=correlation coefficient=-0.524

Answer to part ii).

Since the value of correlation coefficient is -0.524 (i.e., negative) total weight of 3 bananas decreases with increase in total weight of 4 apples.

As they have moderate negative relationship.

Answer to part iii).

Claim of Hilda's husband is false that each week she buys either big apples and big bananas or small apples and small bananas as value of correlation coefficient is negative therefore if one will be bigger than other one will be smaller.

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