statistics problem for one problem in 4 hrs.I will post the problems later………………………………………………………………………………………..

FINAL EXAM
Boyu zhang
Problem 1 (25 points): Independent random samples of 17 sophomores and 13 juniors attending a large university yield the following data on grade point averages:
Sophomore Junior
    3.04
    
    2.56
    1.71
    
    2.77
    3.3
    
    2.7
    2.88
    
    3
    2.11
    
    2.98
    2.6
    
    3.47
    2.92
    
    3.26
    3.6
    
    3.2
    2.28
    
    3.19
    2.82
    
    2.65
    3.03
    
    3
    3.13
    
    3.39
    2.86
    
    2.58
    3.49
    3.11
    2.13
    3.27
At the 5% significance level, do the data provide sufficient evidence to conclude that the mean GPAs of juniors is more than sophomores at this university?
a)    What are the null and alternate hypotheses?
    

Here, and stands for mean GPAs score of population of Sophomores and juniors respectively.
b)    What is the critical value?
    degree of freedom df=17+13-2=28
    
    critical value= -1.7011 (Since it is left tailed test)
c)    What is the Decision Rule?

Reject H0 if t< -1.7011
    
d)    What is the test statistic?

    
    X1
    
 (X1-)^2
     
    X2
    
 (X2-)^2
    3.04
    0.04
     
    2.56
    0.1764
    1.71
    1.2769
     
    2.77
    0.0441
    3.3
    0.2116
     
    2.7
    0.0784
    2.88
    0.0016
     
    3
    0.0004
    2.11
    0.5329
     
    2.98
    0
    2.6
    0.0576
     
    3.47
    0.2401
    2.92
    0.0064
     
    3.26
    0.0784
    3.6
    0.5776
     
    3.2
    0.0484
    2.28
    0.3136
     
    3.19
    0.0441
    2.82
    0.0004
     
    2.65
    0.1089
    3.03
    0.0361
     
    3
    0.0004
    3.13
    0.0841
     
    3.39
    0.1681
    2.86
    0.0004
     
    2.58
    0.16
    3.49
    0.4225
     
    Total=38.75
    Total=1.1477
    3.11
    0.0729
     
     
     
    2.13
    0.5041
     
     
     
    3.27
    0.1849
     
     
     
    Total=48.28
    Total=4.3236
     
     
     
t=-0.8596
e)    What is the decision?
The decision is not to reject the null hypothesis, because -0.8596 is greater than -1.7011.
f)    What does the decision infer?
The data do not provide sufficient evidence to conclude that the mean GPAs of juniors is not more than sophomores at this university.
Excel output:
.................................................
Problem 2 (25 points ): The data below compares the prices of a single hot dog and a medium soft drink at all the Major League Baseball stadia.
    $
    $
    Hot Dog
    Soft Drink
    1
    1
    1.5
    1.5
    2.75
    1.5
    3
    3
    3.25
    3.25
    3.5
    2.5
    3.75
    4
    3.75
    4.5
    4
    4
    4
    4.5
    4.25
    5.25
    4.5
    2.75
    4.5
    4.25
    4.5
    4.5
    4.75
    3.25
    4.75
    4.5
    4.75
    4.75
    5
    4.75
    5
    5
    5
    5.25
    5.25
    4.5
    5.25
    4.75
    5.5
    4
    5.5
    5.75
    6
    4.5
    6.25
    5
a) Draw a scatter Diagram. Let Hot price be the...