Math Project

Statement of the Task This project will be conducted in the form of an investigation that aims to examine the preference of my classmates in fast food. In order to complete this project, I will use data collected from surveys that will be completed by twelfth graders, that have between 17 and 18 years old, of the American School of Tegucigalpa. I will randomly choose fifty students. Once I have gathered all these information, I will count and tally the votes in order to construct all the charts that will visually portray the results of the investigation, depending on the various questions asked in the survey.I will be examining the charts according to each question to determine how often the surveyed people eat fast food, which restaurant they prefer, why, and what is it that they take into account when determining the quality of a fast food restaurant. According to this, I will determine what is it that they are looking in a fast food restaurant.

Then, I will be able to analyze this by interpreting the graphs and comparing them.Throughout the experiment I will also be taking into account possible drawbacks with the method I intend to follow as well as the errors in the liability of the information I intend to gather from my classmates. The conclusion of this experiment will determine what people expect to find in a fast food restaurant and what they take into account when choosing one and determining its quality, which, evidently will play a key role in choosing the best restaurant.Collected Data: Table 1 Do you often eat fast food? | |Female |Male |Total |Percentage | |Yes |20 |6 |26 |52% | |No |13 |11 |24 |48% | |Total |33 |17 |50 | | Table 2 Which one is your favorite? |Male |Female |Total | |Mc Donald's |2 |1 |3 | |Burger King |3 |3 |6 | |Popeye's |6 |5 |11 | |Wendy's |3 |9 |12 | |Quiznos |1 |14 |15 | |KFC |2 |1 |3 | |Total |17 |33 |50 | Table 3 When choosing one, what characteristic do you take most into account? |Male |Female |Total | |Better Taste |2 |7 |9 | |Healthier |3 |5 |8 | |Cheaper |2 |6 |8 | |Most propaganda |2 |3 |5 | |Location |2 |3 |5 | |Cleanness |2 |4 |6 | |Rapidness |2 |2 |4 | |Service |2 |3 |5 | |Total |17 |33 |50 | Table 4 If you had a coupon would you be more likely to visit a fast food restaurant? | |Female |Male |Total |Percentage | |Yes |10 |10 |20 |40% | |No |23 |7 |30 |60% | |Total |33 |17 |50 | | Graphs/Data Analysis Figure 1.

1 [pic]The above graph shows how often the surveyed students eat fast food. The relationship between both genders is shown in this graph. In the case of the females, approximately, 61% of them admitted to often eat fast food, while the rest, 39%, of them answered no to this question. On the other hand, the males appear to eat less fast food than women, as only 35% of them do so. Figure 1. 2 [pic] The above graph represents the choices of the surveyed students on their favorite fast food restaurant.

While the most voted among women was Quiznos, with a 52% of the female votes, the most liked among men was Popeye’s, obtaining a 35% of the votes among the range of men.Surprisingly, as Quiznos was the most liked among women, it was the least liked among men, with only 6% of the male votes. Mc Donald’s and KFC were the least liked among both genders. Figure 1. 3 [pic] This graph represents the votes each characteristic received when participants chose the one they considered most important when it comes to determine the quality of a fast food restaurant.

Among women, the most voted one was “better taste”, with 21% of the votes, while among men, the most voted characteristic was “healthier,” with 18% of the male votes. Figure 1. 4 [pic] Figure 1. 4 shows the male preference on the most important quality that should be taken into account when choosing the best restaurant.The most voted one was “healthier,” while taste did not appear to be very important for men. All the other choices were evenly voted, obtaining all of them 12% of the votes.

However, it is ironic that Quiznos, considering the fact that it offers sandwiches made of vegetables and either chicken, meat, bacon or any other meat, which appears to be much more healthy than hamburgers and french fries, offered by Mc Donald’s and Wendy’s, for example, is the least voted among men, while their preoccupation regarding fast food tends to be how healthy it is. Figure 1. 5 [pic] The above graph shows the most voted aspects taken into account for determining the quality of a fast food restaurant among the surveyed women in this investigation.As the most voted restaurant among women was Quiznos, it was expected that the reason for that is that it appears to offer the healthiest food among all the other restaurants.

Surprisingly, the most voted aspect was “better taste,” not “healthiest. ” The second most voted characteristic was “cheaper,” while “healthier” occupies the third place. Figure 1. 6 [pic] The above graph shows how many of the surveyed people would more likely visit a fast food restaurant if they had a coupon.

Among the male population, the majority, 59% of them, answered yes to this question, while the remaining 41% said no. Among women, 30% of them admitted that they would indeed visit a restaurant if they had a coupon, while 70% of them said no.Once again, it is ironic that, as the preceding graph shows, price occupies the second place on determining the best restaurant, they do not appear to be motivated by coupons. Men, however, are more motivated by discounts that women. Calculating Mean, Median and Mode/ Standard Deviation Better taste: Mean: 12+6 = 9 2 Mode: 9 Standard Deviation: S = ? ( X-X)? = 18 = 18 n-1 1 X X-X (X-X)? 12 3 9 6 3 9 Healthier: Mean: 5+1 = 3 2 Mode: 3 Standard Deviation: S = 8 = 8 1 X X-X (X-X)? 5 2 4 1 2 4 Cheaper: Mean: 1+1 = 1 2 Mode: 1 Standard Deviation: S = 0 = 0 1 X X-X (X-X)? 1 0 0 1 0 0 Most propaganda: Mean: 1+1 = 1 2 Mode: 1 Standard Deviation: S = 0 = 0 1X X-X (X-X)? 1 0 0 1 0 0 Location: Mean: 1+3 = 2 2 Mode: 2 Standard Deviation: S = 2 = 2 1 X X-X (X-X)? 1 1 1 3 1 1 Cleanness: Mean: 8+3 = 5.

5 2 Mode: 5. 5 Standard Deviation: S = 12. 5 = 12. 5 1 X X-X (X-X)? 8 2. 5 6. 25 3 2.

5 6. 25 Rapidness: Mean: 1+1 = 1 2 Mode: 1 Standard Deviation: S = 0 = 0 1 X X-X (X-X)? 1 0 0 1 0 0 Service: Mean: 4+1 = 2. 5 2 Mode: 2. 5 Standard Deviation: S = 4. 5 = 4.

5 1 X X-X (X-X)? 4 1. 5 2. 25 1 1. 5 2.

25 Calculating Expected Table of Frequencies of Fast Food Restaurant Preference According to Gender A.H0: Preference on fast food restaurants is independent of gender group H1: Preference on fast food restaurants is not independent of gender group B. Male: Mc Donald’s 17 x 3 x 50 = 1. 02 50 50 Burger King 17 x 6 x 50 = 2.

04 50 50 Popeye’s 17 x 11 x 50 = 3. 74 50 50 Wendy’s 17 x 12 x 50 = 4. 08 50 50 Quiznos 17 x 15 x 50 = 5. 1 50 50 KFC 17 x 3 x 50 = 1. 02 50 50 Female: Mc Donald’s 33 x 3 x 50 = 1.

98 50 50 Burger King 33 x 6 x 50 = 3. 96 50 50 Popeye’s 33 x 11 x 50 = 7. 26 50 50 Wendy’s 33 x 12 x 50 = 7. 92 50 50 Quiznos 33 x 15 x 50 = 9.

9 50 50 KFC 33 x 3 x 50 = 1. 98 50 50 Observed Table of Frequencies: |Male |Female |Total | |Mc Donald's |2 |1 |3 | |Burger King |3 |3 |6 | |Popeye's |6 |5 |11 | |Wendy's |3 |9 |12 | |Quiznos |1 |14 |15 | |KFC |2 |1 |3 | |Total |17 |33 |50 | Expected Table of Frequencies: |Male |Female |Total | |Mc Donald's |1. 02 |1. 98 |3 | |Burger King |2. 04 |3.

96 |6 | |Popeye's |3. 74 |7. 26 |11 | |Wendy's |4. 08 |7. 92 |12 | |Quiznos |5. 1 |9.

9 |15 | |KFC |1. 02 |1. 8 |3 | |Total |17 |33 |50 | X? calc = ( (? o-? e) ?e X? calc = (2-1. 02)? + (3-2. 04)? + (6-3.

74)? + (3-4. 08)? + (1-5. 1)? + (2-1. 02)? + 1. 02 2.

04 3. 74 4. 08 5. 1 1.

02 (1-1. 98)? + (3-3. 96)? + (5-7. 26)? + (9-7.

92)? + (14-9. 9)? + (1-1. 98)? = 11. 03413817 1.

98 3. 96 7. 26 7. 92 9. 9 1.

98 C. Degrees of Freedom: (Number of rows – 1) (Number of columns – 1) (2-1) x (6-1) = (1) x (5) = 5 Df = 5 p: 0. 0507 D. Critical Value At the 5% level, the critical value is: 11.

070. 11. 70 ; 11. 03 If the x2 calc value is more than the critical value, then we do not accept the null hypothesis. 0. 0507073096 ; 0.

05. If the p value is more than the critical value, then we do not accept the null hypothesis. It is therefore concluded that preference of fast food restaurant preference is dependent on gender. Calculating Expected Table of Frequencies of most important aspects for Fast Food Restaurant According to Gender group A. H0: Preference on best quality fast food restaurants is independent on gender H1: Preference on best quality fast food restaurant is not independent on gender B. Male: Better taste 17 x 9 x 50 = 3.

06 0 50 Healthier 17 x 8 x 50 = 2. 72 50 50 Cheaper 17 x 8 x 50 = 2. 72 50 50 Most propaganda 17 x 5 x 50 = 1. 7 50 50 Location 17 x 5 x 50 = 1.

7 50 50 Cleanness 17 x 6 x 50 = 2. 04 50 50 Rapidness 17 x 4 x 50 = 1. 36 50 50 Service 17 x 5 x 50 = 1. 7 50 50 Female: Better taste 33 x 9 x 50 = 5. 94 50 50 Healthier 33 x 8 x 50 = 5.

28 50 50 Cheaper 33 x 8 x 50 = 5. 28 50 50 Most propaganda 33 x 5 x 50 = 3. 3 50 50 Location 33 x 5 x 50 = 3. 3 50 50 Cleanness 33 x 6 x 50 = 3.

96 50 50 Rapidness 33 x 4 x 50 = 2. 64 50 50 Service 33 x 5 x 50 = 3. 3 50 50 Observed Table of Frequencies: |Male |Female |Total | |Better Taste |2 |7 |9 | |Healthier |3 |5 |8 | |Cheaper |2 |6 |8 | |Most propaganda |2 |3 |5 | |Location |2 |3 |5 | |Cleanness |2 |4 |6 | |Rapidness 2 |2 |4 | |Service |2 |3 |5 | |Total |17 |33 |50 | Expected Table of Frequencies: | |Male |Female |Total | |Better taste |3. 06 |5. 94 |9 | |Healthier |2. 72 |5.

8 |8 | |Cheaper |2. 72 |5. 28 |8 | |Most propaganda |1. 7 |3.

3 |5 | |Location |1. 7 |3. 3 |5 | |Cleanness |2. 04 |3. 96 |6 | |Rapidness |1.

36 |2. 64 |4 | |Service |1. 7 |3. |5 | |Total |17 |33 |50 | X? calc = (2-3.

06)? + (3-2. 72)? + (2-2. 72)? + (2-1. 7)? + (2-1. 7)? + (2-2. 04)? + 3.

06 2. 72 2. 72 1. 7 1. 7 2. 04 (2-1.

36)? + (2-1. 7)? + (7-5. 94)? + (5-5. 28)? + (6-5. 28)? + (3-3.

3)? + (3-3. 3)? + (4-3. 96)? + (2-2. 64)? 1. 36 1. 7 5.

94 5. 28 5. 28 3. 3 3. 3 3.

96 2. 64 + (2-1. 7)? + (7-5. 94)? + (5-5. 28)? + (6-5. 28)? + (3-3.

3)? + (3-3. 3)? + (4-3. 96)? (2-2. 64)? + 1. 7 5. 94 5.

28 5. 28 3. 3 3. 3 3. 96 2. 64 (3-3.

3)? = 1. 58694791 3. 3 C. Degrees of Freedom (Number of rows – 1) (Number of columns – 1) (2-1) x (8-1) = (1) x (7) = 7 Df = 7 p: 0.

979145976 D. Critical Value At the 5% level, the critical value is 14. 067. 1. 5869 ; 14. 0867.

If the x2 calc value is less than the critical value, then we do accept the null hypothesis. Then, it is concluded that preference on the most important aspect taken into account when determining the best fast food restaurant is independent on gender. Evaluation/ConclusionAs proved through the collected data, graphs, data analysis, and chi test in this investigation, I found out what is it that young people, ranging from 17 to 18 years old, look for in a fast food restaurant. As the chi test proved, fast food restaurant preference is dependent on gender. In the case of the most important aspects taken into account when determinig the fast food restaurant of best quality, the math proved it to be independent on gender.

Men appeared to be the most preoccupied with how healthy the food is, whereas women appeared to be more concerned on the taste it has. The most voted qualities were, then, “healthier” and “better taste,” so I oncluded that fast food restaurants should find a way to integrate both aspects in the products they offer, so it would be more liked among young people. The investigation proved to be succesful because all of my classmates I asked to fill the surveyed cooperated very well with me. I learned how to interpret the data and to follow very carefully the steps of the chi test.

I checked and repeated the process many times, so the result would be 100% reliable. I liked very much how math can be applied in proving a hypothesis right or wrong, which makes the results this investigation led to very reliable, as it is based on something as objective as math.