Question

Sleep debt $(3.2)$A researcher reported that the average teenager needs 9.3 hours of sleep per night but gets only $6.3$hours.$17$By the end of a $5$-day school week, a teenager would accumulate about 15 hours of “sleep debt.” Students in a high school statistics class were skeptical, so they gathered data on the amount of sleep debt (in hours) accumulated over time (in days) by a random sample of $25$high school students. The resulting least-squares regression equation for their data is $\stackrel{⏜}{Sleepdebt}=2.23+3.17\left(days\right)$. Do the students have reason to be skeptical of the research study’s reported results? Explain.

Short answer

Yes, students have reason to be dubious of the findings of the research investigation.

Step-by-step solution

Given information

Number of high school students, $n=25$

The resulting least-squares regression equation for their data is,$Sleepdebt=2.23+3.17\left(days\right)$

Concept

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

Explanation

The following is the resultant least square regression line for the data supplied in the question:

$\stackrel{⏜}{sleepdebt}=2.23+3.17\left(days\right)Sˆ$

Thus, we have to evaluate by replacing the days with

as: $\stackrel{⏜}{sleepdebt}=2.23+3.17\left(days\right)$

$$\begin{gathered} =2.23+3.17\left(5\right) \\ =18.08 \end{gathered}$$

As a result, the students have grounds to doubt the findings because their estimated sleep debt exceeds the study's sleep debt of $15$ hours.