Answer to Question #142958 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. (25,5106 ; 27,4591)

Answer 1

Since the population standard deviation is known, normal distribution is used

$CI=\bar{X}\pm Z{_\frac{\alpha}{2}}\frac{\sigma}{n}$

$CI=25\pm Z_{0.025}\frac{5}{\sqrt{40}}$

$Z_{0.025}=1.96$

$CI=25\pm 1.96\frac{5}{\sqrt{40}}$

$=25\pm1.5495$

={23.4505, 26.5495}

Choice 3 is the correct answer.