Standard +0.3 This is a straightforward one-sample t-test with all necessary values provided (sample mean, sum of squared deviations, hypothesized mean, and significance level). Students need to calculate the sample standard deviation, compute the t-statistic, compare with critical value from tables, and state a conclusion. While it requires careful calculation and knowledge of the t-test procedure, it's a standard textbook application with no conceptual challenges or novel problem-solving required, making it slightly easier than average.
6 A random sample of 10 observations of a normal random variable \(X\) has mean \(\bar { x }\), where
$$\bar { x } = 8.254 , \quad \Sigma ( x - \bar { x } ) ^ { 2 } = 0.912 .$$
Using a \(5 \%\) significance level, test whether the mean of \(X\) is greater than 8.05.
6 A random sample of 10 observations of a normal random variable $X$ has mean $\bar { x }$, where
$$\bar { x } = 8.254 , \quad \Sigma ( x - \bar { x } ) ^ { 2 } = 0.912 .$$
Using a $5 \%$ significance level, test whether the mean of $X$ is greater than 8.05.
\hfill \mbox{\textit{CAIE FP2 2012 Q6 [7]}}