Moderate -0.8 This is a straightforward confidence interval calculation with known variance using the z-distribution. It requires only direct application of the standard formula with no conceptual challenges—students simply need to recall the formula, identify n=8, σ²=30, and use the z-critical value 1.96. The calculation is routine with no problem-solving or interpretation required.
1
The continuous random variable \(X\) has the distribution \(\mathrm { N } ( \mu , 30 )\). The mean of a random sample of 8 observations of \(X\) is 53.1 .
Determine a \(95 \%\) confidence interval for \(\mu\). You should give the end points of the interval correct to 4 significant figures.
1\\
The continuous random variable $X$ has the distribution $\mathrm { N } ( \mu , 30 )$. The mean of a random sample of 8 observations of $X$ is 53.1 .
Determine a $95 \%$ confidence interval for $\mu$. You should give the end points of the interval correct to 4 significant figures.
\hfill \mbox{\textit{OCR Further Statistics 2021 Q1 [4]}}