STUDY

In order to create our stratified random sample, we obtained a list of all North Olmsted High School students.  We divided our list into females and males and then randomly generated 100 names from each gender.  After generating the students to be samples, we went to the main office where we looked up student schedules.  We sent the surveys to students' study halls, and possibly their first period if they did not have a study hall.  If they were involved in PSEOP or full time Polaris, we did not send out surveys to those students.  Student and teacher names were written on a post-it with a smiley face so surveys remained anonymous.   We organized our surveys in alphabetical order according to the teachers' last name and Mrs. Caso placed the surveys in the corresponding teachers' mailboxes.  Our population of interest is all of the students who attend North Olmsted High School.

SURVEY

1.     What is your gender?
Male                                Female

2.     Are you familiar with Lady Gaga’s music?
Yes                                  No

3.     If you responded “yes” to the previous question, rate how much you like Lady Gaga on a scale from 1 to 10. (10 being the highest, 1 being the lowest)

          1        2         3          4       5         6         7       8        9        10

DESCRIPTIVE STATISTICS: MALE, FEMALE
          Total
Variable  Count   N  N*  CumN  Percent  CumPct   Mean  SE Mean  TrMean  StDev
M            65  65   0    65      100     100  3.938    0.308   3.780  2.487
F            74  74   0    74      100     100  6.743    0.271   6.864  2.329

                                        Sum of
Variable  Variance  CoefVar      Sum   Squares  Minimum     Q1  Median     Q3
M            6.184    63.14  256.000  1404.000    1.000  2.000   3.000  5.000
F            5.426    34.54  499.000  3761.000    1.000  5.000   7.000  9.000

                                        N for
Variable  Maximum  Range    IQR   Mode   Mode  Skewness
M          10.000  9.000  3.000      1     14      0.71
F          10.000  9.000  4.000  6, 10     12     -0.39

THE SIGNIFICANCE TEST

We are going to use a 2 sample t-test since we want to compare two means, but the population standard deviation is unknown.

µ1 = the true mean rating of Lady Gaga's music for females

µ2 = the true mean rating of Lady Gaga's music for males

Ho: µ1 = µ2      (the average rating of females and males of Lady Gaga's music is about the same)

Ha: µ1 > µ2    (the average rating of females is greater than that of males for Lady Gaga's music)

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

 

n1= 74

n2 = 65

x 1 = 6.74
x 2 = 3.94

s1 = 2.33

s2 = 2.49

t – formula:

t value = 6.83

p- value ≈ 0

degrees of freedom = 131

 

Conclusion:

Since our p-value of approx. 0 is less than alpha, we can reject our null hypothesis at any resonable level of significance.  Therefore, there is sufficient evidence to conclude that in North Olmsted High School, females enjoy Lady Gaga more than males.

 

"But this photo of us, it don't have a price
 ready for those flashing lights" - Paparazzi