Question

1) A random sample is drawn from a population of known standard deviation 10. Construct a 90% confidence interval for the population mean based on the information given n = 36 𝑥 = 100

Answer 1

The critical value for $\alpha = 0.1$ is $z_c = z_{1-\alpha/2} = 1.6449.$

The corresponding confidence interval is computed as shown below:

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

$$=(100-1.6449\dfrac{10}{\sqrt{36}}, \bar{X}+z_c\dfrac{\sigma}{\sqrt{n}})$$

$$=(97.2585, 102.7415)$$

Therefore, based on the data provided, the 90% confidence interval for the population mean is $97.2585 < \mu < 102.7415,$ which indicates that we are 90% confident that the true population mean $\mu$ is contained by the interval $(97.2585, 102.7415).$