<p>The following table shows the weight ($w$) of a foetus, in grams, taken at various weeks ($t$).</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 320px;"><colgroup><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$t$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$12$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$16$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$20$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$24$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$28$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$32$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$36$</p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$w$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$15$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$100$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$300$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$600$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1005$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1700$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$2622$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">Draw a scatter diagram to illustrate the data, labelling the axes clearly.         <span class="inline-marks">[2]</span></div></li></ol>
<p>It is thought that the weight of the foetus at week $t$ can be modelled by one of the formulae</p>
<p style="text-align: center">$w=a+b\ln t$	or	$w=c{{t}^{\text{}\hspace{0.5em}d}}$,</p>
<p>where&nbsp;$a$, $b$, $c$ and $d$ are positive constants.     </p>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Using your scatter diagram, explain which of $w=a+b\ln t$ or $w=c{{t}^{\text{}\hspace{0.5em}d}}$ is the better model.	<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">It is required to estimate the value of $w$ for which $t=30$. Find the equation of a suitable regression line, and use it to find the required estimate, giving your answer to the nearest grams.	<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">It is also required to estimate the value of $t$ for which $w=2000$. Explain whether the regression line of $t$ on $w$ or $\ln t$ on $\ln w$ could be used to find this estimate.  	<span class="inline-marks">[1]</span></div></li></ol>
<p></p>

The following table shows the weight ($w$) of a foetus, in grams, taken at various weeks ($t$).

Draw a scatter diagram to illustrate the data, labelling the axes clearly.         

It is thought that the weight of the foetus at week $t$ can be modelled by one of the formulae

where $a$, $b$, $c$ and $d$ are positive constants.     

Using your scatter diagram, explain which of $w=a+b\ln t$ or $w=c{{t}^{\text{ }d}}$ is the better model.	

It is required to estimate the value of $w$ for which $t=30$. Find the equation of a suitable regression line, and use it to find the required estimate, giving your answer to the nearest grams.	

It is also required to estimate the value of $t$ for which $w=2000$. Explain whether the regression line of $t$ on $w$ or $\ln t$ on $\ln w$ could be used to find this estimate.  	

Hypothesis Testing

International Baccalaureate Higher Level Mathematics

2015 RI P2 Q7

2015 RI P2 Q7