AP Statistics Final Project

Does the average sleep a high school student gets differ between grade levels?

Null Hypothesis: There is no difference in sleep times between underclassmen and upperclassmen at Green Hope High School

Alternate Hypothesis: There IS a difference in sleep times between underclassmen and upperclassmen at Green Hope High School

Summary Statistics

Upperclassmen

Underclassmen

Sample Size 168

Minimum 1.5

Quartile 1 5

Median 6

Mean 6.222917

Quartile 3 7

Maximum 14

Standard Deviation 1.454199516

Graphical Displays

Sample Size: 123

Minimum: 2

Quartile 1: 6

Median: 7

Mean: 6.745935

Quartile 3: 7.625

Maximum: 10

Standard Deviation: 1.351222784

Boxplot

Sampling Technique

Underclassmen

Upperclassmen

• Skewed to the left
• Median:7
• Outliers:2, 2, 3, and 3 hours of sleep
• Spread:8

• Skewed to the right
• Median:6 hours of sleep
• Outliers: 1.5, 11, 12, and 14 hours of sleep
• Spread:12.5 hours of sleep

Conclusion

Populations:

• Green Hope High School underclassmen
• Green Hope High School upperclassmen

Using a numbered list of all the teachers at Green Hope, we randomly selected 10 teachers using a random number generator

We have determined that on a typical school night the true mean sleep hours of underclassmen and underclassmen is different.

This confidence interval suggests that the underclassmen sleep more than the upperclassmen between the range of .197 hours and .849 hours.

This means that underclassmen and upperclassmen get DIFFERENT amounts of sleep

Confidence Interval = Positive

Underclassmen actually get more sleep, on average.

We then surveyed each student in the teacher's second period class. This method of sampling is clustered.

Green Hope students do not get the amount of sleep that they truly and biologically need. The average amount of sleep Green Hope students get on typical school nights seems to decrease as their grade levels increase

Fun Fact!

Both the underclassmen and upperclassmen means were lower than 9.25 hours (which is the amount the National Sleep Foundation suggests for high school students)

Survey

What grade are you in? (circle one) 9 10 11 12

Are you Male or Female? (circle one) Male Female

How many hours of sleep do you get on a typical night (Sunday-Thursday)?

_____________________

Do you have a job? (circle one) Yes No

How many AP classes are you taking? ____________________

Discussion

Assumptions

The Problem

Lurking Variable: Age

Not all of our assumptions were met. Our sample size for the upperclassmen was larger than 10 percent of the population. This means our answers from the standard deviation and margin of error formula could not be correct. We did however perform a simple random sample by assigning each teacher a number and selecting ten numbers with a random number generator.

Underclassmen and upperclassmen not only have different workloads; they also are at different stages of growth. This causes their sleep patterns to vary, and affects both the dependent and independent variable

Confounding Variable: Difficulty of Classes

Underclassmen and upperclassmen are both able to take difficult classes. Hard coursework can effect sleeping habits. Thus, making coursework a lurking variable.

Response Bias

There was response bias because some of the subjects may have not understood the questions on the survey. Also, some people responded with unreasonable answers. For example, someone said they slept 1001 hours per night. We did not include these responses in our data.

Extrapolation

We only feel comfortable extrapolating to Green Hope High School's population. We feel that Green Hope may have a significant difference than the average high school because of its competitive nature and rankings in the state.

Tests

High School Students are faced with heaps of work on a daily basis.Wether it be classwork, projects, lab reports, tests, essays,homework, or even extracurricular activities like jobs or sports, there are many things that can affect student's sleep.

Background Information

The National Sleep Foundation, the American Academy of Pediatrics and many other organizations have conducted research on the amount of sleep students receive.

Statistical Test

Type:

2 Sample T-test (because we do not know the population standard deviations and obtained two sample means)

µ1= the average hours of sleep that underclassmen get on a typical school night

µ2= the average hours of sleep that upperclassmen get on a typical school night

They found that:

• A lack of sleep leads to a increased number of car accidents,mental disabilities, and lower test scores
• 87% of high school students have sleep deprivation
• By delaying the start of school by 30 minutes students receive on average 45 more minutes of sleep

Assumptions

SRS - Good

Sample < or = 10% of population - not met for upperclassmen

n > or = 30 - Good

Confidence Interval

Type: Confidence interval for two sample means

t= 3.15

p-value= .001768

µ1= the average hours of sleep that underclassmen get on a typical school night

µ2= the average hours of sleep that upperclassmen get on a typical school night

Assumptions

SRS - Good

Sample < or = 10% of population - not met for upperclassmen

n > or = 30 - Good

People change as they transition from a freshman to a senior. School work, classes, and sports all change as you get older. Does sleep change as you get older as well?

Interval =

.523 ± .326

We are 95% confident that the true difference between the average sleep times for underclassmen (9th and 10th graders) and upperclassmen (11th and 12th graders) is between .197 and .849 hours.

Is the Average Amount of Sleep on School Nights different for Underclassmen and Upperclassmen at Green Hope High School?