Teach 180: Students Lack of Sleep (Day 102)

Students are naturally more engaged when the topic is of interest to them.  Today's topic in AP Statistics was a review of confidence intervals for a population proportion and our data set was the number of hours of sleep my students got on the first night of school.  I had gathered data from my students on the first day of school using a google form.  I saved the sleep hours column as a .csv file and imported the data into Fathom for us to review.

Next we created a column called "Less_Than_8_Hours" and created the formula at the left to change the quantitative variable to a categorical variable.  If the variable Sleep was less than 8 hours, a "Y" was displayed.  Otherwise an "N" was displayed.  So, what is the point estimate for the proportion of the 47 students surveyed slept less than 8 hours?  And what is the confidence interval?  After we calculated it by hand, we used Fathom to confirm our results.  Our conclusion is that we are 95% confident that the interval from 0.6702 to 0.9042 contains the true proportion of students who slept less than 8 hours the night before school started.  It's crazy to think that students were lacking in sleep even before the school year started!