Are Women Really More Expensive

Than Men?

 

A Taste Test comparing women and men’s preferences of name brand Dr. Pepper to store brand Dr. K.

 

 

 

 

 

 

 

 

 

 

 

Study performed by:  Zach Hatfield, Jackie Hawthorne, and Kristen Cullen.

        Disclaimer:  This study was done in an AP Statistics course with relatively small sample sizes.  The validity of such studies must always be questioned.  Please keep this in mind if you use or report the results of this study.

       

Abstract:  In this experiment, the goal is to prove that a higher proportion of women to men prefer Dr. Pepper to Dr. K.  This implies women tend to have more expensive tastes and therefore would prefer the more costly products than men do.  This outcome is expected because it is stereotypical that women are generally more expensive than men.

        The population used for this experiment is Tates Creek High School students.  The inference was drawn from randomly selected students in the cafeteria during lunch hour.  To assure that bias was reduced a single blind experiment was performed.  The experimenters did not influence the subjects to choose one drink over another. 

        The test performed was a two-proportion z-test. This test shows an observed difference in two populations; therefore it will show if there is a difference between genders’ taste preferences.

         

Methodology:  Is there truly a difference between gender and preference of brands?  Generally females have been associated with higher costs than men; this study will determine whether or not this assumption is true.  To examine this further a taste test was administered to randomly selected male and female subjects.   

        Both Dr. Pepper and Dr. K were purchased and the labels removed.  Dr. K was labeled as “A,” and Dr. Pepper as “B.”  Corresponding labels were placed on the bottom of each cup so the subjects could not see which drink was being tasted. The test was administered in the cafeteria because there was a best chance for the sample to be truly representative of the whole population.  After choosing a location to keep the drinks random selection began.  From each table one student was randomly selected using a random number generator to try each drink and tell which taste was preferred.  This was repeated 20 times, 10 males and 10 females were surveyed.  Usually people with similar tastes associate with one another, therefore friends chose to eat amongst their friends at lunch.  In an attempt to diversify the sample one student per table was chosen.  Time restraints caused a need to change sampling procedures.  On top of the twenty samples previously taken, at least 100 more were needed to provide a big enough sample size to accurately reflect population.  A voluntary response was used to obtain the 100 remaining samples during lunch.  This should not cause bias because the subjects were not aware of what they tasted, therefore the use of single blind sampling reduces voluntary bias.    Because the students were not aware which drink was being tasted and the experimenters did, this was a single blind study.  

Analysis and Inference/Conclusion:

This experiment was to prove that the number of female students who prefer Dr. Pepper was greater than the number of male students.  The test preformed was a two-proportion z test.  The assumptions for a two-proportional z-test are:

 i) Two independent simple random samples

                  ii) Population is at least ten times the sample size; population of Tates Creek is approximately 1,800 students and the sample size used was 120 randomly selected people.

iii)                 N11    60(.5667)=34.002

N22   60(.6)=36

N1 (1-1)  60(1-.5667)=25.998

N2 (1-2)   60(1-.6)=24

 

1=number of women who preferred Dr. Pepper (34/60)

2=number of men who preferred Dr. Pepper (36/60)

H0: P1-P2=0

Ha: P1>P2

P1 is the population of females that prefer Dr. Pepper to Dr. K.

P2 is the population of males that prefer Dr. Pepper to Dr. K.

Test and CI for Two Proportions

 

Sample      X      N  Sample p

1          34     60  0.566667

2          36     60  0.600000

 

Estimate for p(1) - p(2):  -0.0333333

95% lower bound for p(1) - p(2):  -0. 181302

Test for p(1) - p(2) = 0 (vs > 0):  Z = -0.37  P-Value = 0.645

 

Conclusion:

        After running the two-proportion z test, the p-value for women preferring Dr. Pepper more then men was 0.645.  This is not statistically significant to reject Ho at an a=.05 level.  By failing to reject Ho, the experiment shows that there is not a significant difference between women and men’s preference.    Although the p-value is relatively high, if the experiment were to be replicated voluntary response would have been used from the beginning.  This may create different results but would be more effective in sampling a larger number of people.