Standard +0.3 This is a straightforward one-sample t-test with all necessary summary statistics provided. Students need to calculate the sample mean and standard deviation, then apply the standard t-test procedure with given hypotheses. While it requires knowledge of hypothesis testing mechanics, it's a direct application of a standard technique with no conceptual complications or multi-step reasoning beyond the standard algorithm.
7 A random sample of 10 observations of a normally distributed random variable \(X\) gave the following summarised data, where \(\bar { x }\) denotes the sample mean.
$$\Sigma x = 70.4 \quad \Sigma ( x - \bar { x } ) ^ { 2 } = 8.48$$
Test, at the \(10 \%\) significance level, whether the population mean of \(X\) is less than 7.5.
7 A random sample of 10 observations of a normally distributed random variable $X$ gave the following summarised data, where $\bar { x }$ denotes the sample mean.
$$\Sigma x = 70.4 \quad \Sigma ( x - \bar { x } ) ^ { 2 } = 8.48$$
Test, at the $10 \%$ significance level, whether the population mean of $X$ is less than 7.5.
\hfill \mbox{\textit{CAIE FP2 2013 Q7 [7]}}