Respuesta :
Answer:
The 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).
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)}\times \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=24\\\bar x=3.19\ \text{hours}\\s=0.2903\ \text{hours}[/tex]
Confidence level = 99%.
Compute the critical value of t for 99% confidence interval and (n - 1) degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.01/2, (24-1)}=t_{0.005, 23}=2.807[/tex]
*Use a t-table.
Compute the 99% confidence interval for the true mean amount of time Americans spend social networking each day as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
[tex]=3.19\pm 2.807\times \frac{0.2903}{\sqrt{24}}\\\\=3.19\pm 0.1663\\\\=(3.0237, 3.3563)\\\\\approx (3.02, 3.36)[/tex]
Thus, the 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).
