Survey

For my study, the population was all students enrolled in North Olmsted High School. I obtained a list of all the students and used the "sample from columns tool to randomly choose 100 students. I created the survey and looked up the schedules to these 100 students. I sent out the surveys to these students however, many of them could not be reached due to pseop, polaris, or they just no longer attend North Olmsted High School. There was a lot of non response bias too because many of the surveys handed back were filled out incorrectly or not filled out at all.

What is your cumulative gpa? _______________

How many hours of sleep do you get on a typical school night? ___________

Analysis

null hypothesis: There is an association between hours of sleep and grade point average.

alternative hypothesis: There is no asssociation between hours of sleep and grade point average.

μ1=μ2

μ1 ≠ μ2

alpha= .05

assumptions: the samples are independently randomly chosen.

test statistic: two sample t-test

calculation:

Regression Analysis: GPA versus Hours of Sleep

The regression equation is
GPA = 3.45 - 0.0745 Hours of Sleep

Predictor           Coef  SE Coef      T      P
Constant          3.4545   0.5352   6.45  0.000
Hours of Sleep  -0.07453  0.07951  -0.94  0.352

S = 0.656504 R-Sq = 1.5% R-Sq(adj) = 0.0%

Analysis of Variance

Source          DF       SS      MS     F      P
Regression       1   0.3787  0.3787  0.88  0.352
Residual Error  59  25.4288  0.4310
Total           60  25.8075 p-value is 0.352 and the t-value is -0.94 with 60 df. Conclusion- We fail to reject the null hypothesis because the p value is 0.352 which is greater than alpha. Therefore, there is insufficient evidence to say that there is an association between hours of sleep and grade point average.

Unusual Observations

     Hours of
Obs     Sleep     GPA     Fit  SE Fit  Residual  St Resid
18      7.00  4.4000  2.9327  0.0886    1.4673      2.26R
30      4.00  3.8000  3.1563  0.2267    0.6437      1.04 X
42      4.00  2.0000  3.1563  0.2267   -1.1563     -1.88 X
54      7.50  0.9000  2.8955  0.1080   -1.9955     -3.08R

R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.

Descriptive Statistics: GPA, Hours of Sleep

Variable         N  N*    Mean  SE Mean   StDev  Minimum      Q1  Median
GPA             61   0  2.9590   0.0840  0.6558   0.9000  2.5500  3.0000
Hours of Sleep  61   0   6.648    0.136   1.066    4.000   6.000   6.500

Variable            Q3  Maximum
GPA             3.5000   4.4000
Hours of Sleep   7.000    9.000