The daily intakes of milk (in ounces)for ten five-year old children selected at random from one school were: $\begin{array} { l l l l l } 30.3 & 29.6 & 26.3 & 30.0 & 24.0 \end{array}$
$\begin{array} { l l l l l } 30.7 & 31.2 & 24.4 & 28.2 & 27.5 \end{array}$
Find a $99 \%$ confidence interval for the standard deviation, $\sigma$, of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary.
A) $( 1.56,5.33 )$
B) $( 0.58,2.75 )$
C) $( 1.61,5.33 )$
D) $( 1.61,5.93 )$

Question

Quizplus · Accepted Answer

The correct answer is D.The sample standard deviation is s = 2.75 ounces. The sample size is n = 10. The degrees of freedom is df = n - 1 = 9. The critical value for a 99% confidence interval with df = 9 is t* = 3.250. The confidence interval is:s - t* * s/sqrt(n) < σ < s + t* * s/sqrt(n)2.75 - 3.250 * 2.75/sqrt(10) < σ < 2.75 + 3.250 * 2.75/sqrt(10)1.61 < σ < 5.93

The Daily Intakes of Milk (In Ounces)for Ten Five-Year Old 30.329.626.330.024.0\begin{array} { l l l l l } 30.3 & 29.6 & 26.3 & 30.0 & 24.0 \end{array}30.3​29.6​26.3​30.0​24.0​

The Daily Intakes of Milk (In Ounces)for Ten Five-Year Old $\begin{array} { l l l l l } 30.3 & 29.6 & 26.3 & 30.0 & 24.0 \end{array}$