Answer to Question #143276 in Statistics and Probability for Margaret

Question

A simple random sample of 40 items results in a sample mean of 25 . The population standard deviation is a=5 . The 95% confidence interval of the population mean is
1. (25 ; 1,5495)
2. (23,4006 ; 26,5993)
3. (23,4505 ; 26,5495)
4. (23,6679 ; 26,3321)
5. (25,516 ; 27,4591)

Answer 1

We need to construct the 95% confidence interval for the population mean $\mu.$

The following information is provided:

$$\bar{x}=25, \sigma=5, n=20$$

The critical value for $\alpha=0.05$ is $z_c=z_{1-\alpha/2}=1.96.$

The corresponding confidence interval is computed as 

$$CI=(\bar{x}-\sigma\times\dfrac{\sigma}{\sqrt{n}}, \bar{x}+\sigma\times\dfrac{\sigma}{\sqrt{n}})=$$

$$=(25-1.96\times\dfrac{5}{\sqrt{40}}, 25+1.96\times\dfrac{5}{\sqrt{40}})=$$

$$=(23.4505, 26.5495)$$

$3.\ \ \ (23.4505, 26.5495)$