Question

Construct a $90\%$ confidence interval for the population mean weight of the heads of lettuce. State the confidence interval, sketch the graph and calculate the error bound.

Short answer

The class interval$CI:(2.1264,2.2736)$.

Step-by-step solution

Given Information

A $90\%$confidence interval for the population mean weight of the heads of lettuce.

Explanation

Let's find the confidence interval by using the given formula:

$$\begin{gathered} \text{Confidence Interval}=\left[\overline{X}\pm Z_{\frac{\alpha }{2}}\times \frac{\sigma }{\sqrt{n}}\right] \\ =\left[2.2\pm Z_{\frac{0.10}{2}}\times \frac{0.2}{\sqrt{20}}\right] \\ =\left[2.2\pm 1.6449\times \frac{0.2}{\sqrt{20}}\right] \\ =[2.1264,2.2735] \end{gathered}$$

Therefore,$CI:(2.1264,2.2736)$.

The graph:

Error bound: $EBM=0.07$.