SAMPLING: The population of interest is Middle School and High School students and teachers. For the High School studets, we used MINITAB to randomly chose 150 students from all four grade levels.  We used the same process to randomly choose 42 teachers from the high school level. For the middle school teachers, we sent an email to see which teachers were willing to participate. We then went over to the middle school and handed out surveys to classes that were willing to participate. We handed surveys to the teachers who responded to us by email and asked other teachers if they were willing to participate in the study. We received responses from a total of 173 middle schoolers, 79 high schoolers, 29 high school teachers and 21 middle school teachers.

OUR SURVEY: 

Middle/High School Student                                                                                                            

Do you like when teachers put stickers on your graded papers?

Please check only one.

____YES

____NO

Middle/High School Teacher

Do you use stickers when you grade papers on a regular basis?

Please check only one.

____YES

____NO

HYPOTHESIS  TESTS:

MIDDLE SCHOOL TEACHERS VS. HIGH SCHOOL TEACHERS:

1. p1= Middle School Teachers

    p2= High School Teachers

2.  Ho= p1=p2

3. Ha= p1≠p2

4. α= .05

5. Test and CI for Two Proportions: Middle School Teachers, High School Teachers

Event = y

Variable                X   N  Sample p

Middle School Teachers  2  21  0.095238

High School Teachers    5  29  0.172414

Difference = p (Middle School Teachers) - p (High School Teachers)

Estimate for difference:  -0.0771757

95% CI for difference:  (-0.263357, 0.109005)

Test for difference = 0 (vs not = 0):  Z = -0.81  P-Value = 0.417

Fisher's exact test: P-Value = 0.684

6. 29(.05)=1.45

21(.05)=1.05

29(.95)=27.55

21(.95)=19.95

7. Z = -0.81

8. p = 0.684

9. We fail to reject the null hypothesis at the .05 level of significance because our p-value is greater than alpha. Therefore we have sufficient evidence to suggest that there is not a significant difference between the proportion of middle school teachers and high school teachers who like stickers.

Our  conclusion is not valid but would have been valid if our assumptions had been met.

 MIDDLE SCHOOL STUDENTS VS. HIGH SCHOOL STUDENTS:

1. p1= Middle School Students

    p2= High School Students

2.  Ho= p1=p2

3. Ha= p1≠p2

4. α= .05

5. Test and CI for Two Proportions: Middle School Students, High School Students

Event = y

Variable                  X    N  Sample p

Middle School Students  125  173  0.722543

High School Students     62   79  0.784810

Difference = p (Middle School Students) - p (High School Students)

Estimate for difference:  -0.0622668

95% CI for difference:  (-0.174800, 0.0502661)

Test for difference = 0 (vs not = 0):  Z = -1.08  P-Value = 0.278

Fisher's exact test: P-Value = 0.353

6.  79(.05) = 3.95

     173(.05) = 8.65

     79(.95)= 75.05

     173(.95)= 164.35

7. Z = -1.08

8. p= 0.353

9. We fail to reject the null hypothesis at the .05 level of significance because our p-value is greater than alpha. Therefore we have sufficient evidence to suggest that there is not a significant difference between the proportion of middle school students and high school students who like stickers.

Our  conclusion is not valid but would have been valid if our assumptions had been met.

HIGH SCHOOL STUDENTS  VS. HIGH SCHOOL TEACHERS:

1. p1= High School Students

    p2= High School Teachers

2.  Ho= p1=p2

3. Ha= p1≠p2

4. α= .05

5. Test and CI for Two Proportions: High School Students, High School Teachers

Event = y

Variable               X   N  Sample p

High School Students  62  79  0.784810

High School Teachers   5  29  0.172414

Difference = p (High School Students) - p (High School Teachers)

Estimate for difference:  0.612396

95% CI for difference:  (0.447736, 0.777057)

Test for difference = 0 (vs not = 0):  Z = 7.29  P-Value = 0.000

Fisher's exact test: P-Value = 0.000

6. 29(.05) =

79(.05) =

29(.95) =

79(.95) =

7. Z = 7.29

8. p = 0.000

9. We can reject the null hypothesis at the .05 level of significance because our p-value is less than alpha. Therefore we have sufficient evidence to suggest that there is a significant difference between the proportion of middle school teachers and high school teachers who like stickers.

Our  conclusion is not valid but would have been valid if our assumptions had been met.

MIDDLE SCHOOL STUDENTS  VS.  MIDDLE SCHOOL TEACHERS:

1. p1= Middle School Students

    p2= Middle School Teachers

2.  Ho= p1=p2

3. Ha= p1≠p2

4. α= .05

5. Test and CI for Two Proportions: Middle School Students, Middle School Teachers

Event = y

Variable                  X    N  Sample p

Middle School Students  125  173  0.722543

Middle School Teachers    2   21  0.095238

Difference = p (Middle School Students) - p (Middle School Teachers)

Estimate for difference:  0.627305

95% CI for difference:  (0.485130, 0.769481)

Test for difference = 0 (vs not = 0):  Z = 8.65  P-Value = 0.000

Fisher's exact test: P-Value = 0.000

6.  21(.05) = 1.05

     173(.05) = 8.65

     21(.95) = 19.95

     173(.95) = 164.35

7. Z = 8.65 

8. p=0.000

9. We can reject the null hypothesis at the .05 level of significance because our p-value is less than alpha. Therefore we have sufficient evidence to suggest that there is a significant difference between the proportion of middle school students and high school students who like stickers.

Our  conclusion is not valid but would have been valid if our assumptions had been met.