A small cafe sells one type of coffee. The selling price of a cup of coffee is reviewed and adjusted

Question

A small cafe sells one type of coffee. The selling price of a cup of coffee is reviewed and adjusted at the beginning of every year depending on market conditions. Based on sales figures collected over $7$ years, the cafe owner, Mr Tay, studied the effect of the selling price of a cup of coffee, , on the average number of cups, $y$ cups, sold per day within the year. The data is shown in the table below.

$x$	$2.0$	$2.2$	$2.5$	$3.0$	$4.0$	$4.4$	$4.5$
$y$	$280$	$250$	$190$	$150$	$90$	$100$	$70$

On the grid in the Printed Answer Booklet, draw a scatter diagram of the data.[2]

Mr Tay realised that one of the values of $y$ has been wrongly stated in the data table.

Indicate the corresponding point on your diagram by labelling it $P$. Explain why the scatter diagram for the remaining points may be consistent with a model of the form $y=a+\frac{b}{x}$, where $a$ and $b$ are constants.[2]
Omitting $P$, calculate the product moment correlation coefficient and the least squares estimates of $a$ and $b$ for the model $y=a+\frac{b}{x}$.[2]
Use the model $y=a+\frac{b}{x}$ with the values of $a$ and $b$ found in part (c) to estimate the value of $y$ that has been wrongly stated in the data table. Give two reasons why you would expect this estimate to be reliable.[3]

Accepted Answer

(a) Scatter diagram shown (b) $P=(4.4,100)$, reciprocal model (c) $r=0.997$, $a=-101$, $b=757$ (d) $y=71.2$ cups, reliable

2025 RI P2 Q8

2025 RI P2 Q8

Video Solution:

Solution:

Solution locked