Answer to Question #282343 in Statistics and Probability for saad

Question

x = 5410 , n=65, s=680 find 90% confidence interval for μ.

Answer 1

The critical value for $\alpha = 0.1$ and $df = n-1 = 64$ degrees of freedom is $t_c = z_{1-\alpha/2; n-1} = 1.669013.$

The corresponding confidence interval is computed as shown below:

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

$$=(5410-1.669013\times\dfrac{680}{\sqrt{65}},$$

$$5410+1.669013\times\dfrac{680}{\sqrt{65}})$$

$$=(5269.2294, 5550.7706)$$

Therefore, based on the data provided, the 90% confidence interval for the population mean is $5269.2294 < \mu < 5550.7706,$ which indicates that we are 90% confident that the true population mean $\mu$ is contained by the interval $(5269.2294, 5550.7706).$