Moderate -0.8 This is a straightforward application of the standard confidence interval formula for a normal distribution with known variance. It requires only direct substitution into the formula CI = x̄ ± z*σ/√n with no conceptual challenges or multi-step reasoning—purely routine calculation that any well-prepared student should execute quickly.
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{SPS SPS FM Statistics 2024 Q1 [4]}}