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Chapter 4: Q 43. (page 230)

Sleep debt (3.2)A researcher reported that the average teenager needs 9.3 hours of sleep per night but gets only 6.3hours.17By the end of a 5-day school week, a teenager would accumulate about 15 hours of 鈥渟leep debt.鈥� 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 25high school students. The resulting least-squares regression equation for their data is Sleepdebt铃�=2.23+3.17(days). Do the students have reason to be skeptical of the research study鈥檚 reported results? Explain.

Short Answer

Expert verified

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

Step by step solution

01

Given information

Number of high school students, n=25

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

02

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.

03

Explanation

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

sleepdebt铃�=2.23+3.17(days)S藛

Thus, we have to evaluate by replacing the days with

as: sleepdebt铃�=2.23+3.17(days)

=2.23+3.17(5)=18.08

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.

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