Respuesta :
Answer:
The 95% confidence interval for the population mean height of young adult females is (64.8 inches, 66.0 inches).
Step-by-step explanation:
Let X = heights of young adult females in the United States.
The standard deviation of the heights of young adult females in the United States is, σ = 2.6 inches.
A sample of n = 85 young adult females at BYU-Idaho is selected.
The sample mean height of these 85 females is, [tex]\bar x=65.4\ inches[/tex].
The (1 - α)% confidence interval for the population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}[/tex]
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
Compute the 95% confidence interval for the population mean height of young adult females as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\=65.4\pm1.96\times \frac{2.6}\sqrt{85}}\\=65.4\pm 0.553\\=(64.847, 65.953)\\\approx(64.8, 66.0)[/tex]
Thus, the 95% confidence interval for the population mean height of young adult females is (64.8 inches, 66.0 inches).
