<ol class="abc-list"><li><div class="list-item-paragraph">Sketch a diagram that might be expected when&nbsp;$x$ and $y$ are related approximately by $y=a+b\ln x$ in each of the cases <strong>(i)</strong> and <strong>(ii) </strong> below. In each case your diagram should include 6 points, approximately equally spaced with respect to $x$, and with all $x$- and $y$-values positive.</div><ol class="i-list"><li><div class="list-item-paragraph">$a$ and $b$ are both positive.	<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">$a$ is positive and $b$ is negative.<span class="inline-marks">[1]</span></div></li></ol></li><li><div class="list-item-paragraph">In a chemical reaction, the yield of a chemical compound, $m$ grams, at different temperature ${{t}^{\circ }}$ C are given in the table below.</div><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>$t$</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>$15$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$22$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$27$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$31$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$35$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$40$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$45$</p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$m$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.83$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$3.02$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$4.67$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$13.96$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$5.67$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$8.07$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$8.35$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$8.60$</p></td></tr></tbody></table></div><ol class="i-list"><li><div class="list-item-paragraph">Draw the scatter diagram for these values, labelling the axes clearly.	<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">One of the pairs of data appears to be recorded wrongly. Indicate the corresponding point on your diagram by labelling it $P$, and explain why the scatter diagram for the remaining points may be consistent with a linear model.	<span class="inline-marks">[2]</span></div><div class="list-item-paragraph">For the rest of the questions, omit $P$ in your calculation.</div></li><li><div class="list-item-paragraph">Calculate the equation of the least squares regression line of $m$ on $t$.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">When the data $t=50$and $m=k$ was obtained and added to the seven pairs of data above, the new regression line is $m=0.16934t+0.72035$ correct to $5$ decimal places. Find the value of $k$, giving your answer in $2$ decimal places.	<span class="inline-marks">[3]</span></div></li></ol></li></ol>

Sketch a diagram that might be expected when $x$ and $y$ are related approximately by $y=a+b\ln x$ in each of the cases **(i)** and **(ii) ** below. In each case your diagram should include 6 points, approximately equally spaced with respect to $x$, and with all $x$- and $y$-values positive.

In a chemical reaction, the yield of a chemical compound, $m$ grams, at different temperature ${{t}^{\circ }}$ C are given in the table below.

Hypothesis Testing

International Baccalaureate Higher Level Mathematics

2015 MJC P2 Q9

2015 MJC P2 Q9