Pictures and Quotes

 

Dance first.  Think later.  It's the natural order.  ~Samuel Beckett

The Study

In order to create our sample, we obtained the list of students who attended the 2009 Winter Formal dance at North Olmsted High School. We then used our random number generator on mini-tab to randomly select 160 students from the Winter Formal list that we had already acquired. After selecting the 160 students, we went to the main office to look up each student’s study hall so we could send them a survey. If the selected student didn’t have a study hall, we sent it to their third period class. If the student didn’t have a study hall or a third period class due to PSEOP or Polaris, we sent it to a random class. Once we looked up all of the classes, we organized them alphabetically by teacher. Then Mrs. Caso placed the surveys in the corresponding teacher’s mailboxes. Our population of interest is all of the students who attend North Olmsted High School. The sample consists of students who attended the 2009 Winter Formal dance. We didn’t include students that attended Polaris or PSEOP full-time.

 

Survey

Please answer the following questions as honestly and accurately as possible.  The results will be used in a project for my statistics class.  The results will be anonymous.

 

1.  What is your gender?       MALE       FEMALE

 

3.  What grade are you in?       9       10       11       12

 

2.  Did you attend the 2009 Winter Formal Dance?       YES       NO

 

3.  If you did attend the 2009 Winter Formal, did you have a date?       YES       NO

 

4.  If you answered no to the previous question, approximately how many people did      you dance with? (Please be as accurate as possible!)     _______________

 

Descriptive Statistics: Partners for Girls

Variable N N* Mean SE Mean StDev Minimum Q1 Median

Number of Partners for G 74 0 5.797 0.718 6.173 1.000 1.000 5.000

Variable Q3 Maximum

Number of Partners for G 8.250 40.000

 

Descriptive Statistics: Partners for Boys

Variable N N* Mean SE Mean StDev Minimum Q1 Median

Number of Partners for B 56 0 4.250 0.645 4.829 1.000 1.000 1.000

Variable Q3 Maximum

Number of Partners for B 7.500 20.000

Based upon the Descriptive statistics gathered from Minitab, it appears that the average number of dance partners for females exceeds that of males by  1.547.  The standard deviation for the number of dance partners for females also exceeds that of males, but by 1.344.  This shows that the female sample has a higher average for the number of dance partners.  Also, there is more variability within the female sample.

 

The Significance Test

We are going to use a two-sample t-test since we want to compare two means, but the population standard deviation is unknown.

µ1 = the true mean number of dance partners for girls who attended the 2009 Winter Formal.

µ2 = the true mean number of dance partners for boys who attended the 2009 Winter Formal.

Ho: µ1 = µ2      (the average number of dance partners for females is equal to that of male)

Ha: µ1 < µ2    (the average number of dance partners for females is less than that of                      males)

α = 0.05

Assumptions:

  1. Both samples are independently selected random samples
  2. Both populations are normally distributed since both n1 and n2 are greater than 30

à  Since the population standard deviation is unknown, we must use the t-test instead of            the z-test!

n1= 74

n2 = 56

1 = 5.797

2 = 4.250

s1 = 6.173

s2 = 4.829

t – formula:

t value = 1.602992616

p- value = .1114041725

degrees of freedom = 127.8417508

Conclusion:

Since our p value is greater than alpha, we failed to reject the null hypothesis at a significance level of .05. Therefore, there is insufficient evidence to say that the true mean number of dance partners for males who attended the 2009 Winter Formal is greater than the true mean number of dance partners for females who attended the 2009 Winter Formal.