Standard +0.3 This is a straightforward application of the one-sample t-test and confidence interval formula with standard steps: calculate sample mean and standard deviation, find the t-statistic, compare to critical value, then construct the confidence interval. All procedures are routine for Further Maths Statistics with no conceptual challenges or novel problem-solving required, making it slightly easier than average.
A random sample of 8 observations of a normal random variable \(X\) gave the following summarised data, where \(\overline{x}\) denotes the sample mean.
$$\Sigma x = 42.5 \quad \Sigma(x - \overline{x})^2 = 15.519$$
Test, at the 5% significance level, whether the population mean of \(X\) is greater than 4.5. [7]
Calculate a 95% confidence interval for the population mean of \(X\). [3]
A random sample of 8 observations of a normal random variable $X$ gave the following summarised data, where $\overline{x}$ denotes the sample mean.
$$\Sigma x = 42.5 \quad \Sigma(x - \overline{x})^2 = 15.519$$
Test, at the 5% significance level, whether the population mean of $X$ is greater than 4.5. [7]
Calculate a 95% confidence interval for the population mean of $X$. [3]
\hfill \mbox{\textit{CAIE FP2 2012 Q9 [10]}}