Respuesta :
Answer:
The 90% confidence interval for population mean length of eastern rods is (23.73, 24.07).
Step-by-step explanation:
The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\ \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=25\\\bar x=23.9\ \text{feet}\\s=0.50\ \text{feet}\\t_{\alpha/2, (n-1)}=t_{0.05, 24}=1.71\\[/tex]
Compute the 90% confidence interval for population mean length of eastern rods as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\ \frac{s}{\sqrt{n}}[/tex]
   [tex]=23.9\pm 1.71\times\frac{0.50}{\sqrt{25}}\\\\=23.9\pm 0.171\\\\=(23.729, 24.071)\\\\\approx (23.73, 24.07)[/tex]
Thus, the 90% confidence interval for population mean length of eastern rods is (23.73, 24.07).
