Respuesta :
Answer:
The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 37 - 1 = 36
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 36 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0262
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0262\frac{5}{\sqrt{37}} = 1.67[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 31 - 1.67 = 29.33 minutes
The upper end of the interval is the sample mean added to M. So it is 31 + 1.67 = 32.67 minutes.
The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.
