Q.13 - The Practice of Statistics for AP

Question

A milk processor monitors the number of bacteria per millilitre in raw milk received at the factory. A random sample of 10 one-millilitre specimens of milk supplied by one producer gives the following data:

5370 4890 5100 4500 5260 5150 4900 4760 4700 4870

Construct and interpret a 90% confidence interval for the population mean $\mu$.

Step-by-Step Solution

Answer

The confidence interval for the population mean $\mu$ is $(4794.4,5105.6)$

Step 1: introduction

A milk processor monitors the number of bacteria per millilitre in raw milk received at the factory.  

Given data - 

$5370 4890 5100 4500 5260 5150 4900 4760 4700 4870$

Step 2: explanation

Calculating the confidence interval CI,

n = $10$

$\stackrel{-}{x}=4950$ and s = $268.45$

$$\begin{gathered} \Rightarrow \overline{x}\pm z\frac{s}{\sqrt{n}} \\ =4950\pm 2.021\frac{268.45}{\sqrt{10}} \\ =(4794.4,5105.6) \end{gathered}$$

the confidence interval is $(4794.4,5105.6)$