Answer:
The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).
Step-by-step explanation:
The (1 - α) % confidence interval for population mean (μ) is:
[tex]CI=\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]
Here the population standard deviation (σ) is not provided. So the confidence interval would be computed using the t-distribution.
The (1 - α) % confidence interval for population mean (μ) using the t-distribution is:
[tex]CI=\bar x\pm t_{\alpha /2,(n-1)}\frac{s}{\sqrt{n}}[/tex]
Given:
[tex]\bar x=27.97\\s=10.04\\n=25\\t_{\alpha /2, (n-1)}=t_{0.01/2, (25-1)}=t_{0.005, 24}=2.797[/tex]
*Use the t-table for the critical value.
Compute the 99% confidence interval as follows:
[tex]CI=27.97\pm 2.797\times\frac{10.04}{\sqrt{25}}\\=27.97\pm5.616\\=(22.354, 33.586)\\\approx(22.35, 33.59)[/tex]
Thus, the 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).
