The mean weight of trucks traveling on a particular section of Highway 401 is not known. A provincial highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. What is the 95 percent interval for the population mean?
A) 14.7 and 16.9
B) 13.2 and 17.6
C) 10.0 and 20.0
D) 16.1 and 18.1

Question

Quizplus · Accepted Answer

To calculate the 95% confidence interval for the population mean, we use the formula for the confidence interval of the mean with known sample mean ($\bar{x}$), sample standard deviation (s), and sample size (n). The formula is $\bar{x} \pm z \frac{s}{\sqrt{n}}$, where $z$ is the z-score corresponding to the desired confidence level (for 95%, $z = 1.96$). Given $\bar{x} = 15.8$, $s = 3.8$, and $n = 49$, the margin of error is $1.96 \times \frac{3.8}{\sqrt{49}} = 1.96 \times \frac{3.8}{7} = 1.96 \times 0.542857 \approx 1.1$. Adding and subtracting this margin of error from the sample mean gives us the interval $15.8 \pm 1.1$, which is $14.7$ to $16.9$.

The Mean Weight of Trucks Traveling on a Particular Section