Answer
μ is between 0.82 and 3.38. The Atkins program doesn't seem to be effective or practical because the weight loss is not too much.
Work Step by Step
$\alpha=1-0.9=0.1.$ $\sigma$ is 3.8, hence we use the z-distribution with $df=sample \ size-1=40-1=39$ in the table. $z_{\alpha/2}=t_{0.05}=1.685.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.685\cdot\frac{4.8}{\sqrt{40}}=1.28.$ Hence the confidence interval:$\mu$ is between 2.1-1.28=0.82 and 2.1+1.28=3.38. The Atkins program doesn't seem to be effective or practical because the weight loss is not too much.
