Question

Researchers are concerned about the impact of students working while they are enrolled in classes, and they would like to know if students work too much and therefore are spending less time on their classes than they should be. First, the researchers need to find out, on average, how many hours a week students are working. A survey of 50 students provides a sample mean of 7.1 hours worked with the standard deviation of 5 hours. What is a 95% confidence interval based on this sample

Answer 1

Answer:

The 95% confidence interval based on this sample is between 5.9 and 8.3 hours.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

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 = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$. So we have T = 1.68

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.68\frac{5}{\sqrt{50}} = 1.2$

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 7.1 - 1.2 = 5.9 hours

The upper end of the interval is the sample mean added to M. So it is 7.1 + 1.2 = 8.3 hours.

The 95% confidence interval based on this sample is between 5.9 and 8.3 hours.