Question

Students in a statistics class are conducting a survey to estimate the mean number of hours each week that students at their college study. The students collect a random sample of 49 students. The mean of the sample is 12.2 hours. The standard deviation is 1.6 hours. Use the T-distribution Inverse Calculator applet to answer the following question. What is the 95% confidence interval for the number of hours students in their college study?

Answer 1

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 $1 - \frac{1 - 0.95}{2} = 0.975$. 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.