Coca-Cola s Secret Formula Internationally Variable?

Transcription

1 Coca-Cola s Secret Formula Internationally Variable? 0

2 Introduction On May 8, 1886, Dr. John Pemberton invented the first formula for the well-known soft drink Coca-Cola. Starting out as a local product costing approximately 5 cents per glass and selling about 9 drinks a day, Coca Cola has since expanded to a multibillion-dollar company mass producing and marketing its famous product all over the world. 1 Down through the years, there has been much excitement precipitated over Coca-Cola s secret formula. 2 While the Coca-Cola company has apparently never officially devolved an exact list of Coca-Cola s ingredients, it is certain that they have done a lot of tweaking of the big secret. Numerous versions have appeared, including New Coke, Coke Zero, diet Coke, and vanilla Coke. Recently, with Coca-Cola being produced in many different counties, people have questioned whether or not the famous cola might taste different in different countries. Some people firmly assert that there is a difference, while others suggest that it is all the same, but apparently no one has done a careful study of the question. 3 This Study proposes to address the following questions: Can people tell the difference between Coca-Cola produced in China and Coca-Cola produced in the United States by correctly pairing cups of a similar kind? If so, what proportion prefers which kind, Do people of one gender tend to do better then people of another gender at telling the difference between the Coca-Cola from China and the U.S., and Are people from the U.S. better or worse at differentiating between U.S. and Chinese Coca- Cola than Chinese people? Procedure Before beginning testing on subjects, four 600 ml-size bottles of Chinese Coca-Cola were purchased and transported to the U.S. in the author s checked luggage. Soon afterwards, a corresponding 4 bottles of U.S. Coca-Cola were purchased to be paired off with the Chinese cola. Bottles from both countries were all labeled as Coca-Cola, and were not marked vanilla, cherry or any other flavor. The U.S. bottles were marked as Coke original formula and the Chinese bottles were simply marked Coke. The different bottles should have represented common, plain Coca-Cola as it is marketed in their respective countries. Other preliminary materials included a place mat (see Appendix 1) and a large number of small, identical, disposable paper cups. Testing was done in groups of at least 2 and at most 8 people. A bottle of U.S. and a bottle of Chinese cola would be selected and placed in the same area of a refrigerator to cool. Four small cups would be numbered 1 through 4 and placed in their proper places on the place mat. For each cup, starting with the first, a penny was flipped to see if it should have U.S. or Chinese cola. If the penny came up heads, that cup would receive U.S. cola, if tails, Chinese. Once two cups had been assigned any one kind of cola, the remaining cup(s) would be For example: 3 There has been plenty of informal discussion/speculation on the subject. For examples: and I have not found any example of a formal study of the question. 1

3 designated the opposite type. For example, if the penny came up heads, tails, heads, the penny would not be flipped for the fourth cup; by default, cup 4 would receive Chinese cola. The type of cola each cup would receive was recorded for each subject's place mat. Cola was added to the cups according to assignment. This type of randomized assignment for each individual subject had two benefits. First, subjects could not cheat by asking each other which cups they thought tasted similar. Second, it enforced variation in which cups were pairs. If two pairings of cups (for example, 1,2=Chinese and 3,4=U.S.) had been randomly selected and then used for all subjects, it might possibly have occurred that the pairing hit upon was of a kind that people would naturally pair off the cups to. In the example of Chinese being 1,2 and U.S. being 3,4, it could be possible that a majority proportion of people, when they have no idea which cups are which, will make one pair of the top cups and one pair of the bottom cups (see Appendix 1 place mat for placing of cups). While this kind of human influenced random guess selection may not indeed exist, randomized assignment for each subject guarded against its possible influence. Subjects would then be gathered (usually to be seated at a table). Gender was noted down for each subject. Data was also collected on what age range each subject fell into. The following script would be read to them: You have before you 4 cups. Two contain Chinese Coca-Cola, and two contain American Coca-Cola. Your task is to match the cups that contain the same kind of cola. Once you have matched them, please indicate which pair of cups contains the cola that you like better. If you feel that there is no difference among the cups, do not worry about it. Just match the cups to the best of your ability and choose one of the pairs as the Coca-Cola type you like best. If anyone had questions, they could be asked and answered before starting into taste testing. Simple, clarifying statements about the instructions were often also made, but the subjects were in no way informed of which cups contained which kinds of cola. This method of administration firstly, informed subjects that there were two different pairs of Coca-Cola cups in front of them, and, secondly, forced subjects to guess at those pairs and select one pair as better. A more complex study might have left open the possibility that there were, for example, 3 cups of Chinese Coca-Cola and one of U.S. on the place mat or that all the cups were the same. The U.S. to Chinese cups ratio in this study was fixed to keep things simple. Therefore, in interpretation of results, it must be kept in mind that people were differentiating between U.S. and Chinese Coca-Cola, after being told that there was definitely two kinds of Coca-Cola in front of them. Also, people were forced to choose one pair of cups as their preferred kind. They were not allowed to consider both colas equally good. Once all the subjects had finished pairing the cups and checking the boxes for the pair they preferred, their pairs and preferences were recorded with the record of which cups had which cola for their particular place mat. Effort was made to ensure that for almost all testing batches a sufficient number of subjects (usually more than 6) were gathered at one time to use up the two bottles that were originally placed in the refrigerator to cool together. 4 This was because, after initially breaking the seal on a bottle, slightly different amounts of shaking, opening and closing might have caused one bottle to become less fizzy than the other. Subjects might then be able to pair cups based on their differing amounts of fizzyness. Thus, they might have been discriminating between different treatments of the bottles not an actual difference in taste between U.S. and Chinese Coca-Cola. Information was collected on subjects both in China and America. Though the above description was for U.S. subjects, the procedure, using translated script and place mats (see 4 Only about 4 subjects were not served from freshly opened bottles. 2

4 appendices 1 and 2), was essentially the same in China. The author, being able to speak Chinese as well as English, administered the tests in both countries. Question 1: Can people tell the difference between Coca-Cola from China and Coca-Cola from the United States by correctly pairing cups of a similar kind? Of the 54 people from whom data was collected, 28 correctly paired the cups. Pie Chart of Cup Pairing Success Category Correct Incorrect Incorrect 48.1% Correct 51.9% Total sample size: 54 For a test of significance, technically speaking, our population of interest would be all people. Our parameter of interest is what proportion of all people can tell the difference between U.S. and Chinese Coca-Cola. For this study, this means all those who can correctly separate two randomly placed pairs of cups one pair containing U.S. Coca-Cola and the other Chinese Coca-Cola. The null hypotheses is that the proportion of people who can pair the cups is 1/3. If one cup is selected out of the four and then another cup is randomly selected out of the remaining three, the probability that the second cup will match the first is 1/3. (There are three cups left, and only one of them contains the same cola as the cup already selected.) Thus the probability that you would correctly divide the cups into matching pairs would be 1/3. Thus, the null hypothesis predicts that only about 1/3 of all people could correctly pair the cups. The alternate hypothesis states that more than 1/3 of all people can correctly pair the cups. H a suggests that people are not just randomly guessing; some proportion of them can tell the difference between U.S. and Chinese Coca-Cola, and that proportion is greater than 1/3. H 0 : p=1/3 The proportion of all people that will correctly pair the cups is 1/3 H a : p>1/3 The proportion of all people that will correctly pair the cups is greater than 1/3 3

5 To test the null hypotheses, a one-sample z-test for a proportion will be used. The three conditions for this test are: 1. The population is at least 10 times as large as the sample. Condition met. Samples size times 10 is 54*10= is vastly smaller than the world s population of ~6 billion people. 2. Sample size times null hypotheses proportion, p 0, is 10 or more, and (1-p 0 ) times sample size is 10 or more. Condition met. 54*(1/3)=18 and 54*(2/3)= The data are a Simple Random Sample from the population of interest. Condition NOT met. Data, in both China and America, was collected on people available to the author. Results may not accurately represent the population of interest, and must be interpreted with this in mind. This will be true for all inference preformed in this report. The z statistic is: z = p p 0 p0(1 p0) n p =.519 p =.333 n = z = = (1.333) 54 Z=2.90 corresponds to a p-value of This means that, if H 0 were true, in all possible samples of people with a sample size of n=54, only about 0.19% of the samples would come up with a proportion of successes as large or larger than the proportion in this study is less than 0.05 so at α=0.05 the results are considered statistically significant. H 0 is rejected. Some proportion of all people can tell the difference between U.S. and Chinese Coca-Cola and that proportion is greater than 1/3. In order to estimate the proportion of all people who can differentiate between U.S. and Chinese Coca-Cola, a one-sample z-interval for a population proportion can be formed. The conditions are the same as for the inference just conducted except for the second one: 4

6 2. Sample size times sample proportion must be >9. Samples size times 1 minus sample proportion must be >9. Condition met: 54*.519=~28 and 54*(1-.519) = ~26. Keeping in mind that we are not dealing with a SRS, we proceed with forming a confidence interval. (1 ) p z * p ± p n p =.519 n = 54 z = (1.519).519 ± 1.96* =.519 ± The resulting 95% confidence interval for the true population proportion is from.39 to % confidence means that in the sampling distribution of the population of interest for samples of size n=54, 95% of the samples would include the true population proportion in their 95% confidence intervals. Thus it may be concluded with 95% confidence that between 39% and 65% of all people can correctly distinguish between U.S. and Chinese Coca-Cola by pairing off cups of the same kind. Question 2: If so, what proportion prefers which kind? Of the 28 people who correctly paired the cups containing Chinese and American Coca-Cola, 7 preferred U.S. Coca-Cola while the remaining 21 preferred Chinese Coca- Cola. Pie Chart of Kind of Coca-Cola Preferred Preferred U.S. Cola 25.0% Category Preferred Chinese Cola Preferred U.S. Cola Preferred Chinese Cola 75.0% Total sample size: 28 5

7 The population of interest for this confidence interval is all people who can tell the difference between U.S. and Chinese Coca-Cola. The parameter of interest is what proportion of these people prefer Chinese Coca-Cola. (It might also be of interest what proportion prefer U.S. Coca-Cola. However, because more people in this study preferred Chinese Coca-Cola, they will be focused on). Again, a one-sample z-interval for a population proportion can be formed. The conditions are: 1. The population is at least 10 times as large as the sample. Condition met: Samples size times 10 is 28*10=280. Using the bottom edge of the confidence interval for what proportion of all people can tell the difference, a total population size of at least (~6 billion)*(.39)=2.34 billion people can be estimated billion is far larger than Sample size times sample proportion, p-hat, is greater >9, and (1 p-hat) times sample size is >9. Condition NOT met. 28*(.75)=21 and 28*(.25)=7. 7 is less than 9. Thus, the sampling distribution for our sample size may not be very close to normal. This could lead to an inaccurate confidence interval, and must be remembered in the interpretation of results. 3. The data are an SRS from the population of interest. Condition NOT met. This study did not obtain a SRS. We proceed with caution to form a 95% confidence interval: (1 ) p z * p ± p n p =.750 n = 28 z = (1.750).750 ± 1.96* =.750 ± The resulting 95% confidence interval for the true population proportion is from 0.59 to Thus it may be concluded with 95% confidence that between 59% and 91% of all people who can correctly distinguish between U.S. and Chinese Coca-Cola prefer Chinese Coca-Cola. If this confidence interval is representative of the population of interest (failures in meeting conditions render this dubious), it would indicate that more than half of all people who can tell the difference between U.S. and Chinese Coca- Cola prefer Chinese Coca-Cola. This might be interesting to the Coca-Cola company if it were to consider marketing the Chinese version of Coca-Cola outside of China. 6

8 Question 3: Do people of one gender tend to do better at telling the difference between the Coca-Cola s from China and from the U.S.? Of the 54 people who were tested, 24 were male and 30 were female. Among females, 12 (40.0%) correctly paired the cups and among males, 16 (~66.7%) correctly paired the cups. Percent Correct/Incorrect Within Each Gender Male Female Category Correct Incorrect Correct 66.7% Correct 40.0% Incorrect 33.3% Incorrect 60.0% Percent Correct/Incorrect Within Each Gender Percent Correct or Incorect Gender Percent within levels of Gender. Correct Incorrect Female Correct Incorrect Male 7

9 This large difference in percent success rates may indicate that males tend to be slightly better at telling the difference between U.S. and Chinese Coca-Cola than females. The appropriate test for this question is a two-sided two-proportion z-test. (A one-sided test could be preformed if the author had suggested that males could tell the difference better than females prior to obtaining the results of the study; however, this was not the case.) The populations of interest are all males and all females. The parameters of interest are what proportion of each group can tell the difference between U.S. and Chinese Coca-Cola. The null hypothesis states that the proportion of males who can tell the difference is the same as the proportion of females. The alternate hypothesis states that the proportions are different. H 0 : p males correct = p females correct The proportion of all males who can pair the cups correctly equals the proportion of all females who can pair the cups correctly. H a : p males correct p females correct The proportion of all males who can pair the cups correctly does not equal the proportion of all females who can pair the cups correctly. The conditions for testing are: 1. Both populations are at least 10 times as large as the sample. Condition met: There are far more than 240 males and 300 females in the world s population 2. For both samples, sample size times pooled sample proportion, p-hat, is 5 or more and (1 p-hat) times sample size is 5 or more. Condition met: pooled sample proportion is: (13+15) successes/(28+30) total attempts= *(.519)=15.6, 24*(.519)=12.5, 30*(1-.519)=14.4, and 24*(1-.519)= The samples are independent SRS s from the respective populations of interest. Condition NOT met. This study did not obtain a SRS. z = ( p p ) males correct females correct 1 1 p(1 p) + nmales n females p =.667 p =.400 p =.519 n males correct males = 24 n = 30 females females correct ( ) z = = (1.519)

10 The corresponding p-value is This means that in about 5.1% of all two such samples, we would expect them to have proportions as far or farther apart then was the case in this study is significant at α=.10, but it just misses significance at α=.05. Therefore, at α=.05 we do not reject the null hypotheses. At the same time, there is evidence that males perform differently from females. If H 0 were true, in only about 5.1 out of every 100 such pairs of samples would such a large difference be seen between male and female success rates. Question 4: Are people from the U.S. better or worse at differentiating between U.S. and Chinese than Chinese people? Twenty five subjects were from the U.S. and twenty nine were from China. 15 of the 25 from the U.S. paired correctly, and 13 of 29 from China succeeded. Pie Charts of Correct/Incorrect for Chinese/Americans Chinese U.S. Category Correct Incorrect Correct 44.8% Correct 60.0% Incorrect 55.2% Incorrect 40.0% 9

11 Percent Correct/Incorrect for Each Nationality Percent Correct or Incorrect Correct Incorrect Nationality Chinese Percent within levels of Nationality. Correct Incorrect U.S. Again, to address our question we can use a two-sided two-proportion z-test. The populations of interest are all Chinese and all U.S. people. The parameters of interest are what proportion of each group can tell the difference between U.S. and Chinese Coca- Cola. The null hypothesis, H 0, is that the proportion of Chinese who can tell the difference is the same the proportion of Americans. The alternate hypothesis states that the proportion of Chinese and Americans who can tell the difference is different. H 0 : p Chinese correct = p Americans correct The proportion of all Chinese who can pair the cups correctly equals the proportion of all Americans who can pair the cups correctly. H a : p Chinese correct p Americans correct The proportion of all Chinese who can pair the cups correctly does not equal the proportion of all Americans who can pair the cups correctly. The conditions for testing are the same as for gender comparison: 1. Both populations are at least 10 times as large as the sample. Condition met: There are far more than 25*10=250 U.S. citizens and far more than 29*10=290 Chinese people 2. For both samples, sample size times pooled sample proportion, p-hat, is 5 or more, and (1 p-hat) times sample size is 5 or more. Condition met: pooled sample proportion is (13+15) succeses/54 total attmpts= *(.519)=15.1, 25*(.519)=13.0, 29*(1-.519)=13.9, and 25*(1-.519)= The samples are independent SRS s from the respective populations of interest. Condition NOT met. This study did not obtain any SRS s. 10

12 z = ( p p ) Americans correct Chinese correct 1 1 p(1 p) + namericans n Chinese p =.600 p =.448 Americans correct Chinese correct p =.519 n = 25 n = 29 Americans Chinese ( ) z = = (1.519) The corresponding p-value is This is not significant even at α=0.10. There is not good evidence that Chinese and Americans have different abilities in distinguishing between U.S. and Chinese Coca-Cola. At the same time, there was a difference in percent success rates for Chinese and Americans in this study (~15%), and it may be that sample size was simply insufficient to obtain statistical significance. Further research in this area might prove informative. Conclusion It appears that there is a difference in taste between U.S. and Chinese Coca-Cola. This experiment tried to detect that difference by seeing if people could correctly create a pair of U.S. Coca-Cola cups and a pair of Chinese Coca-Cola cups out of 4 cups. A sufficient proportion of people succeeded to make it convincing that they were not just guessing at the matches. This indicates that, at least when people are prompted about a difference among the cups, some proportion of them can distinguish a difference. Most people who could tell the difference between the two kinds of cola preferred Chinese Coca-Cola. This might indicate that Chinese Coca-Cola would be more marketable than U.S. Coca-Cola; however, there is an interesting possible reason this could be false: quantity. Consumers do not buy little Dixie cups of Coca-Cola in supermarkets and drink only 2 or 3 ounces at a time. They buy bottles and drink (relatively) large quantities over (relatively) extended periods of time. Elements of flavor involving cumulative sweetness and aftertaste 5 may cause matching little cups to be somewhat unrepresentative of buying big bottles. This is open to question. From this study, there is good evidence (though not quite significant at α=0.05) that males on average are much better at differentiating between U.S. and Chinese Coca- Cola than females. One possible reason for this is that males tend to drink more soda then females. 6 A greater familiarity with the subtleties of the taste of Coca-Cola as it is marketed in the subject s respective countries would probably prove an advantage in 5 It seems to the author as well as to some of his subjects that Chinese Coca-Cola is sweeter than U.S. Coca-Cola. The author also believes that Chinese Coca-Cola has a more distinct (and incidentally unpleasant) after-taste. 6 Males usually seem to drink more soda than females. For example, see 11

13 distinguishing between U.S. and Chinese Coca-Cola. It is possible that Americans are better at distinguishing U.S. and Chinese Coca-Cola than Chinese are, but further study with larger samples is necessary to confirm this. Suggestions for Improvement on this Study Νumber each subject s sheet so that each subject s number can be written with the records of which of his/her cups contained Chinese/U.S. Coca-Cola. This would have made keeping track of things easier and cut down on the possibility of a mix up causing one subject s response to be put with a different subject s records of which cups contained U.S./Chinese Coca-Cola. On each sheet make a place for each subject to record his/her gender, and indicate his/her appropriate age range (Note: this study collected data on age range, though sample size was not sufficient to conduct inference. See Avenues for Further Research.) This would also have helped things run more smoothly and efficiently. Ensure that the cups could all be filled with their proper Coca-Cola s in a room separate from the subjects. During the study, some subjects eagerly stopped to see what the administrator was doing before he was ready for them. This resulted in having to shoo them away and also in their possibly seeing what Coca-Cola was going into what cups. If everything was set up in a separate room before subjects were brought in, this problem could be eliminated. A substance for clearing the palate should be considered. Subjects were not provided with anything, and therefore may have found it harder to distinguish the cups. Two (male) subjects were observed coming up with their own palate-cleansers (one used some chips and the other used some water). Self-conducted palate-clearing clearly introduced a potential confounding variable. Finally, future studies would benefit from obtaining a Simple Random Sample instead of opportunistically selecting subjects. While a true SRS is almost impossible to gather, by narrowing the population of interest to something more manageable than all people (for example, a given region of U.S. or China), some attempt at selecting a random sample might have been implemented. Even a rough approximation of an SRS would make all the inference in this study more meaningful and less open to question. Avenues for Further Research As noted in the explanation of procedure, data was collected on subjects age. Each subject was placed in a 10 year age range. The lowest age range used was years, and the highest was years. Age Range (in years) Number of People Paired Cups Correctly Number of People Paired Cups Incorrectly

14 Bar Chart of Percent Success For Each Age Group Percent Success Years Old 10 denotes years, 20 denotes years, and so on Unfortunately, due to small sample size, chi-square analysis on this data would not be meaningful. Two of the expected counts are less than 1 and most of them are less than 5. In order to determine whether or not people of different age ranges tend to be better or worse at pairing cups, a study with a much larger sample size needs to be conducted. It would also be informative to conduct a study in which subjects were given identical looking bottles of Chinese and U.S. Coca-Cola and allowed to drink from all four bottles over the course of a day before responding as to which bottles they thought were a pair and which pair they preferred. This might shed some light on the question of whether preferences expressed during little cup taste-testing are representative of people s actual predilections. Such a study would be relatively hard to do, however. A third area of possible future research would be conducting studies of whether or not a larger proportion of males can tell the difference between U.S. and Chinese Coca- Cola than females. While the obtained p-value of.051 indicates that this is probably true, larger studies might be able to more strongly confirm the difference with a smaller p- value. Finally, it might also be interesting to collect information on whether or not participants were habitual Coca-Cola drinkers of their own countries Coca-Cola, to see whether or not there is a relationship between normal Coke consumption and ability to distinguish between U.S. and Chinese Coca-Cola. Acknowledgements First and foremost, I would like to thank my AP Statistics teacher Mrs. for giving me an excellent introduction into the wonderful world of statistics without which I never would have been able to undertake this project. I would also like to thank her specifically for looking over my report several times and answering some of my 13

15 questions. Second, I would like to thank Dr. for discussing the design of the project with me. Finally, I would like to thank my family for help in brainstorming about the project and for general support during its implementation. I would also like to thank my father for giving helpful comments on the report. 14

16 Appendix 1 Place mat (English version) 15

17 Place mat (Chinese version) 16

18 Appendix 2 Chinese version of script 在 你 面 前 有 四 个 杯 子 其 中 两 杯 是 中 国 可 乐, 另 外 两 杯 是 美 国 可 乐 你 要 做 的 就 是 把 包 含 同 一 种 可 乐 的 杯 子 进 行 配 对 你 配 对 好 了 以 后, 请 在 方 框 内 打 勾 表 明 你 更 喜 欢 哪 对 杯 子 里 的 可 乐 如 果 你 觉 得 四 个 杯 子 里 的 可 乐 都 没 有 区 别, 不 用 在 意 只 要 尽 力 把 这 些 杯 子 进 行 配 对, 并 且 选 择 一 对 作 为 你 更 喜 欢 的 可 乐 (Translated in collaboration with a native Chinese Speaker.) Age Range Gen der Correct or Incorrect Preferred Kind Appendix 3 Raw Data Cups With Chinese Coca-Cola Cups With U.S. Coca- Cola Subject s Pair #1 (In cases when subject s pairs did not match the U.S. and Chinese Cola pairs) U.S. Sample F Incorrect 1,2 3,4 1,3 2, M Correct Chinese 1,3 2, F Correct Chinese 1,4 2, M Correct Chinese 1,3 2, F Correct Chinese 1,2 3, M Incorrect 1,3 2,4 1,2 3, F Incorrect 1,3 2,4 2,3 1, F Incorrect 2,3 1,4 1,2 3, F Correct Chinese 1,2 3, F Incorrect 3,4 1,2 1,4 2, F Incorrect 3,4 1,2 1,4 2, F Incorrect 2,3 1,4 3,1 2, F Correct U.S. 1,2 3, M Correct U.S. 1,3 2, F Correct U.S. 2,3 1, M Correct Chinese 3,4 1, M Correct Chinese 2,3 1, M Correct Chinese 2,4 1, F Incorrect 3,4 1,2 1,4 2, M Incorrect 2,4 1,3 1,2 3,4 Subject s Pair # 2 (In cases when subject s pairs did not match the U.S. and Chinese Cola pairs) 17

19 60-69 M Correct Chinese 1,2 3, F Correct Chinese 1,4 2, F Correct U.S. 2,4 1, M Correct Chinese 2,3 1, F Incorrect 3,4 1,2 1,3 2,4 Chinese Sample M Incorrect 3,4 1,2 1,3 2, M Incorrect 1,4 2,3 1,2 3, M Incorrect 3,4 1,2 2,3 1, M Correct Chinese 1,2 3, F Incorrect 2,3 1,4 1,2 3, F Incorrect 3,4 1,2 3,1 2, F Incorrect 2,4 1,3 3,2 1, M Incorrect 1,4 2,3 3,4 1, F Correct Chinese 2,3 1, F Incorrect 1,2 3,4 1,3 2, F Incorrect 1,2 3,4 1,3 2, F Incorrect 2,4 1,3 1,4 2, F Correct Chinese 3,4 1, F Incorrect 1,2 3,4 1,3 2, F Correct Chinese 2,4 1, M Incorrect 1,4 2,3 1,2 3, M Incorrect 1,3 2,4 3,4 1, F Correct Chinese 1,3 2, F Correct U.S. 2,4 1, M Correct Chinese 1,4 2, M Correct U.S. 3,4 1, F Incorrect 1,2 3,4 3,1 2, M Correct U.S. 1,2 3, F Incorrect 3,4 1,2 1,4 2, M Correct Chinese 1,4 2, M Correct Chinese 2,3 1, M Correct Chinese 1,4 2, M Correct Chinese 1,2 3, F Incorrect 1,2 3,4 1,4 2,3 18