Standard +0.3 This is a straightforward application of a t-distribution confidence interval with small sample size. Students must calculate sample mean and standard deviation from given data, then apply the standard formula with t₇ critical value. While it requires careful arithmetic and knowledge of the t-distribution, it's a routine textbook exercise with no conceptual challenges or novel problem-solving required.
1 A scientist is investigating the lengths of the leaves of a certain type of plant. The scientist assumes that the lengths of the leaves of this type of plant are normally distributed. He measures the lengths, \(x \mathrm {~cm}\), of the leaves of a random sample of 8 plants of this type. His results are as follows.
\(\begin{array} { l l l l l l l l } 3.5 & 4.2 & 3.8 & 5.2 & 2.9 & 3.7 & 4.1 & 3.2 \end{array}\)
Find a \(90 \%\) confidence interval for the population mean length of leaves of this type of plant.
1 A scientist is investigating the lengths of the leaves of a certain type of plant. The scientist assumes that the lengths of the leaves of this type of plant are normally distributed. He measures the lengths, $x \mathrm {~cm}$, of the leaves of a random sample of 8 plants of this type. His results are as follows.\\
$\begin{array} { l l l l l l l l } 3.5 & 4.2 & 3.8 & 5.2 & 2.9 & 3.7 & 4.1 & 3.2 \end{array}$
Find a $90 \%$ confidence interval for the population mean length of leaves of this type of plant.\\
\hfill \mbox{\textit{CAIE Further Paper 4 2024 Q1 [4]}}