<p>A weight is suspended in mid-air by means of a string of length $x$ cm. In an experiment, the weight was displaced slightly and the time, $y$ s, taken to complete $10$ oscillations was recorded. The results are shown in the table.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$x$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$10$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$30$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$50$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$100$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$150$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$200$</p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$y$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$7.05$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$9.85$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$15.53$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$18.86$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$25.91$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$28.31$</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.<span class="inline-marks">[1]</span></div></li></ol>
<p>It is thought that the time taken $y$ can be modelled by one of the formulae $y=a+bx$ or $y=c+d\sqrt{x}$ where&nbsp;$a$, $b$, $c$ and $d$ are constants.</p>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Find the value of the product moment correlation coefficient between</div><ol class="abc-list"><li><div class="list-item-paragraph">$y$ and $x$,</div></li><li><div class="list-item-paragraph">$y$ and $\sqrt{x}$.<span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-paragraph">Use your answers to <strong>(i)</strong> and <strong>(ii)</strong> to explain which formula is the better model.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Find the equation of a suitable regression line and use it to estimate the value of $y$ when&nbsp;$x=45$. Comment on the reliability of the estimate.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">The addition of a data point will not change the equation of the regression line found in <strong>(iv)</strong>. State the coordinates of such a point.<span class="inline-marks">[1]</span></div></li></ol>

A weight is suspended in mid-air by means of a string of length $x$ cm. In an experiment, the weight was displaced slightly and the time, $y$ s, taken to complete $10$ oscillations was recorded. The results are shown in the table.

Draw a scatter diagram to illustrate the data.

It is thought that the time taken $y$ can be modelled by one of the formulae $y=a+bx$ or $y=c+d\sqrt{x}$ where $a$, $b$, $c$ and $d$ are constants.

Find the value of the product moment correlation coefficient between

Use your answers to **(i)** and **(ii)** to explain which formula is the better model.

Find the equation of a suitable regression line and use it to estimate the value of $y$ when $x=45$. Comment on the reliability of the estimate.

The addition of a data point will not change the equation of the regression line found in **(iv)**. State the coordinates of such a point.

Hypothesis Testing

International Baccalaureate Higher Level Mathematics

2015 YJC P2 Q10

2015 YJC P2 Q10