A laboratory tested 78 chicken eggs and found that the mean amount of cholesterol was 224 milligrams with $s = 14.7$ milligrams. Find the $95 \%$ confidence interval.
A) $220

Question

A laboratory tested 78 chicken eggs and found that the mean amount of cholesterol was 224 milligrams with $s = 14.7$ milligrams. Find the $95 \%$ confidence interval.
A) $220 < \mu < 226$
B) $221 < \mu < 227$
C) $222 < \mu < 228$
D) $220 < \mu < 227$

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: $\bar{x} \pm z \times \frac{s}{\sqrt{n}}$. Here, $\bar{x} = 224$, $s = 14.7$, $n = 78$, and $z$ for 95% confidence is approximately 1.96. Calculating gives $224 \pm 1.96 \times \frac{14.7}{\sqrt{78}}$, which results in the interval $221 < \mu < 227$.

A Laboratory Tested 78 Chicken Eggs and Found That the Mean