Question

Suppose that the weights (in kgs) of six months old babies, monitored at a healthcare facility, have $N(\mu, \sigma^2)$ distribution, where $\mu \in \mathbb{R}$ and $\sigma > 0$ are unknown parameters. Let $X_1, X_2, \ldots, X_9$ be a random sample of the weights of such babies. Let $\overline{X} = \frac{1}{9} \sum_{i=1}^{9} X_i$, $S = \sqrt{\frac{1}{8} \sum_{i=1}^{9} (X_i - \overline{X})^2}$ and let a 95% confidence interval for $\mu$ based on $t$-distribution be of the form $(\overline{X} - h(S), \overline{X} + h(S))$, for an appropriate function $h$ of random variable $S$. If the observed values of $\overline{X}$ and $S^2$ are 9 and 9.5, respectively, then the width of the confidence interval is equal to __________ (round off to 2 decimal places) (You may use $t_{9,0.025} = 2.262, t_{8,0.025} = 2.306, t_{9,0.05} = 1.833, t_{8,0.05} = 1.86$).

Answer 1

The correct Answer is : 4.70 -4.80(Approx.)