library(s20x)
sleepDeprivation.df = read.table("sleepDeprivation.txt", header = TRUE)
plot(SleepHrs ~ Deprived, data = sleepDeprivation.df)
summaryStats(SleepHrs~ Deprived, data= sleepDeprivation.df)
Sample Size Mean Median Std Dev Midspread
No 35 7.057143 7 1.161714 1.5
Yes 50 6.060000 6 1.057722 1.0
The median hours of sleep for the non-deprived group is 7, whereas it is 6 for those who are deprived. The range is 3-9 hours for the former and 3-10 for the latter. The data for both groups appear to lack any sort of skew.
onewayPlot(SleepHrs ~ Deprived, data = sleepDeprivation.df)
eovcheck(SleepHrs ~ Deprived, data = sleepDeprivation.df)
sleepNo = with(sleepDeprivation.df, SleepHrs[Deprived == "No"])
sleepYes = with(sleepDeprivation.df, SleepHrs[Deprived == "Yes"])
sleep2samp.df = data.frame(sleepHrs = c(sleepNo, sleepYes))
state = c(rep("No",35),rep("Yes",50))
normcheck(lm(sleepHrs ~ state, data = sleep2samp.df))
t.test(sleepHrs ~ state, data = sleep2samp.df, var.equal=TRUE)
Two Sample t-test
data: sleepHrs by state
t = 4.1075, df = 83, p-value = 9.329e-05
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.5143015 1.4799842
sample estimates:
mean in group No mean in group Yes
7.057143 6.060000
Method and Assumptions:
We have a numerical measurement made on two distinct groups, so we should do a two-sample t-test. We assume the survey respondents are independent of one another. The equality of variance assumption looks to be satisfied according to the one-way-plot, likewise with normality of distribution as seen in the Q-Q plot. Thus, the standard two-sample t-test is appropriate.
The model fitted is sleepHrs = µ+αi+εij, where αi is the effect of whether the student reported to be sleep deprived or not, either changed or present, and εij iid ∼ N(0,σ2).
Executive Summary:
This study was undertaken to see if there was a difference in the number of hours of slept among students who reported to be sleep deprived and students that did not. We estimated the mean hours of sleep for non-deprived students to be between 31 minutes and 1 hour 28 minutes more than students who claimed to be sleep deprived.
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