91Ó°ÊÓ

How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (in centimeters per year) over a severalyear period at locations in the Gulf of Mexico and the Caribbean. Here are the data for the Gulf of Mexico: 9 $$ \begin{array}{l|llllll} \hline \text { Mean sea surface temperature } & 26.7 & 26.6 & 26.6 & 26.5 & 26.3 & 26.1 \\ \hline \text { Growth } & 0.85 & 0.85 & 0.79 & 0.86 & 0.89 & 0.92 \\ \hline \end{array} $$ (a) Do the data indicate that coral growth decreases linearly as mean sea surface temperature increases? Is this change statistically significant? (b) Use the data to predict with \(95 \%\) confidence the mean coral growth (centimeters per year) when mean sea surface temperature is \(26.4^{\circ} \mathrm{C}\).