Question

Use technology and the given confidence level and sample data to find the confidence interval for the population mean mu. Assume that the population does not exhibit a normal distribution. Weight lost on a diet:
99 % confidence
n equals 41
x overbar equals 4.0 kg
s equals 6.1 kg

Answer 1

Answer: (1.55, 6.45)

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline\ {x}\pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Significance level : $\alpha: 1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Sample size : n=41

Sample mean : $\overline{x}=4.0\text{ kg}$

Standard deviation : $\sigma=6.1\text{ kg}$

Then, 99% confidence interval for population mean will be :_

$4\pm\ (2.576)\dfrac{6.1}{\sqrt{41}}\\\\\approx4\pm2.45\\\\=(4-2.45, 4+2.45)=(1.55, 6.45)$