Answer:
The 95% confidence interval for the number of hours students in their college study is between 8.98 hours and 15.42 hours.
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 = 49 - 1 = 48
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 48 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0106
The margin of error is:
M = T*s = 2.0106*1.6 = 3.22
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 12.2 - 3.22 = 8.98 hours.
The upper end of the interval is the sample mean added to M. So it is 12.2 + 3.22 = 15.42 hours.
The 95% confidence interval for the number of hours students in their college study is between 8.98 hours and 15.42 hours.
