Is The Proportion Of Customers With A Child In The Vehicle That Choose To Use The Drive-Thru Greater Than The Proportion Of Customers With A Child In The Vehicle That Choose To Order From The Inside Dining Area Of The McDonalds In Newton, MA Between 11:30 am and 1:30 pm On A Saturday?

Michael Johnsen (2007)

05/26/05

Buckingham Browne & Nichols School
Cambridge, MA
May 2005

Table of Contents......................................................................... 2

Abstract........................................................................................... 3

Study............................................................................................... 4

Research Question................................................................................................ 4

Sampling................................................................................................................. 4

Data......................................................................................................................... 6

Significance Test................................................................................................... 7

Magnitude.............................................................................................................. 9

Discussion.................................................................................... 10

Weaknesses in the Study................................................................................... 10

Extrapolation....................................................................................................... 10

Conclusion................................................................................... 12

Abstract

In the following study, the proportions of customers of a McDonalds with children in their vehicle that ordered from the drive-thru and that ordered from the inside dining area were compared. The main goal of the study was to give the restaurant any information on the types of customers that order from the drive-thru more for the purpose of advertising. If a significant result was found, then the restaurant might want to advertise to the family audience that it has a drive-thru. It was expected that the population proportion that ordered from the drive-thru would be higher than the population proportion that ordered from the inside dining area because it is easier for a guardian with a child in the car to not have to unfasten the child and potentially deal with tantrums in the restaurant.

After performing a Two Sample Z-Test of Significance, it was discovered that the sample provided no evidence to reject the null hypothesis that the proportion of customers with children in the vehicle ordering from the drive-thru was equal to the proportion that ordered from the inside dining area (n_Drive-Thru = 40, n_Inside = 40, p = 0.18066). The magnitude of the results was calculated by constructing a 95% confidence interval. Because the test did not provide significant evidence to reject the null hypothesis at the level, it was known that zero would be included in the interval (-0.1136, 0.3136).

The two samples were taken from the McDonalds in Newton, MA on a Saturday between 11:30 am and 1:30 pm. A child was to count for the sample as a success if it was sitting in a car seat or booster seat. This caused the major weakness in the sampling process because there was no definite age limit of the children that were considered “children” for the samples. This could have contributed to the sample not providing any evidence to reject H_o.

Study

Research Question

Based on the results of this observational study, I will compare the difference between two proportions. The proportions are from the population of vehicles with children in them that park allowing any of the occupants to go into the inside dining area of the McDonalds and order their food and the proportion of vehicles with children in them that order from the drive-thru. Both populations only include data from between 11:30 am and 1:30 pm on Saturday.

I would expect the proportion of customers with children in their vehicles that choose to order from the drive-thru to be higher than the proportion of customers that choose to order from the inner dining area. I expect this result because it is easier and safer for guardians with children in the car to go through the drive-thru because he/she does not have carry the child into the restaurant and deal with the kicking, screaming, and other hassles a child could potentially make. Also, the parent would not have to worry about the safety of the child if it was left in the car.

Sampling

The data for the samples of this study were collected from two populations of customers that eat at the McDonalds in Newton, MA between 11:30 am and 1:30 pm on Saturday. The populations were the proportion of customers that had children in their vehicle that either ordered from the drive-thru or the inside dining area. This site and time were ideal conditions for my study because Newton is a residential area where there are many young families with children. I was able to find many subjects because many families were going out to lunch at the specified time. Even if the families were not going out for lunch together, there will still be many children that would have been taken out to lunch by either guardians of the child, relatives, or friends.

To collect data I sat in my car, which was parked in the middle row of the lot between the entrance to the McDonalds and the dining area of the McDonalds (diagram 1). From my vantage point, I was able to see if the vehicle went through the drive-thru (picture 1). If the vehicle went through the drive-thru, the subject’s data was used for the “drive-thru” sample. If the vehicle did not go through the drive-thru, the subject was used for the “inside dining area” sample. From my vantage point, I was not able to see if the customer actually ordered from the drive-thru, but I could see if the customer picked up the order from the pick-up window (picture 2). If a subject did not pick up a meal from the pick-up window, then it was counted as ordering from the inside dining area.

Once the sample that the subject belonged to was determined, I determined if there was a child so that the vehicle could be considered a success for the sample. From my vantage point, if I could not determine whether there definitely was or was not a child, the subject was rejected. A subject was considered to have a child in the backseat that counted as a child for the sample if it was sitting in a car seat designed for children, or a booster seat integrated into the car designed for children.

For the purposes of randomization, I did not use every subject observed in the original sample. For the sample of customers going through the drive-thru, I assigned each subject a two-digit number between 01 and 85. For the sample of customers ordering from the inside dining area, I assigned each subject a number between 01 and 75. Then separately for each sample, I used a random digits table to select a new sample of 40 subjects. 1 For every two digits the generator output, I corresponded them to one of the subjects.2 If a number that was generated did not correspond to a subject, it was rejected and a new pair was generated. If a number was repeated, it was rejected and a new pair was generated.

The reason for randomization is because there might have been a caravan of families and/or friends that might have been coming from a previous event, such as a bar/bat mitzvah or reunion. In this case, they might all have chosen to order from the interior counter, but if the family came alone they might have chosen to use the drive through. Also, some families might have been be too large to fit in one car. In this case, there might have been two cars, one with at least one child in it, and one car with no children in it. This would have resulted in a false-negative result for the car with no children in it, no matter which means of getting the food the family chose.

Data

See attached appendix

Significance Test

Hypothesis:

–>The true population proportion of customers with children in their vehicle that go through the drive-thru is equal to the true proportion of customers with children in their vehicle that order from the inside dining area at the McDonalds in Newton between 11:30 am and 1:30 pm on a Saturday.

–>The true population proportion of customers with children in their vehicle that go through the drive-thru is greater than the true proportion of customers with children in their vehicle that order from the inside dining area at the McDonalds in Newton between 11:30 am and 1:30 pm on a Saturday.

Two Proportion Z-Test Of Significance:

Symbols:

= Drive-Thru Sample Size

= Inside Dining Area Sample Size

= Proportion of the combined number of children in the vehicle of

customers who go through the drive-thru and who order from the inside dining area

= Sample Proportion of customers who order from the drive-thru

= Sample Proportion of customers who order from the inside dining

area

Conditions:

1. Both samples are independently selected simple random samples : √

Z-Test Statistic: Graph:

P-Value:

Significant at : X

Conclusion:

The sample provides no evidence to reject the null hypothesis (n_Drive-Thru = 40, n_Inside = 40, p = 0.18066). Thus, the true population proportion of customers with children on their vehicle is equal for the customers who order from the drive-thru and the inside dining area.

Magnitude

Two Proportion Z-95% Confidence Interval

Conditions:

1. Both samples are independently selected simple random samples : √

2. Customers going through drive-thru10 –> 40 10 : √

Customers ordering from inside dining area 10 –> 40 10 : √

Interval:

Conclusion:

I can say with 95% confidence that the difference between the true proportions of customers with children in their vehicle who order from the drive-thru and who order from the inside dining area falls between the interval (-0.1136, 0.3136). I can also conclude that if I were to take 100 samples with the same sample sizes as in these samples, approximately 95 of them would be included in this interval (-0.1136, 0.3136).

Discussion

Weaknesses in the Study

There were a few weaknesses in the sampling process that may have influenced the results collected. The most important is the way in which children were deemed to be “children” for the study. Subjects were considered to children if they were sitting in a car seat, because the goal of the study was to show that parents or guardians would be more likely to take a child in a car seat through the drive-thru rather than unstrapping them from the car seat and ordering for them from the inside dining area. The weakness comes from the fact that there are different ages for children who travel in car seats. Some children stop traveling in car seats as young as three years old, but others may still in car seats or booster seats until they are as old as seven. Thus, there may have been children who could have been considered to count as “children” for the sample, but were not because they did not actually travel in a car seat. The opposite scenario could also have easily taken place, with an older child who did not mature as quickly as he or she should have matured. In this case, the child would have been counted when it was actually older than the targeted age for the study.

Extrapolation

The results from this study can be extrapolated represent a population that is bigger than the one observed. The population of all McDonalds in suburban, residential areas with the option of ordering from a drive-thru can be represented. This is due to the fact that in Newton, where the sample was selected, there are many places for families with children to get together and have an occasion for going out to lunch before hand or afterwards. If the different locations have a similar proportion of customers with children in the vehicle, then they should distribute themselves similarly when ordering from the drive-thru or the inside dining area.

The results from this study cannot however be extrapolated to represent a population that includes customers ordering outside the observed time on the observed day. This is because the Saturday lunch hour is probably the busiest time for customers with children because during the week, the children are most likely to be at school. Also, on Sunday there are probably going to be fewer children eating with their parents because there are obligations they may have to their family and or religion. The results can also not represent any other time on Saturday because for the morning hours of the day, children are likely to be sleeping because they tend to sleep longer than adults. Also, kids tend not to go out very much at night when they are very young, especially if the parents are not present and the child is under supervision of a guardian.

Conclusion

My alternative hypothesis that the true population proportion of customers of the McDonalds in Newton, MA between 11:30 am and 1:30 pm on a Saturday with children in their vehicle that ordered from the drive-thru would be greater than the proportion that ordered from the inside dining area was unable to be accepted after analyzing the data. The test that provided no evidence to reject the null hypothesis at the level had a z test statistic of (z=0.9129) and a p-value of (p=0.18066). A 95% confidence interval was also performed to support the conclusion found from the significance test. Because the test was not significant at the level, it was known that zero would be included in the 95% confidence interval, which was calculated to be (-0.1136, 0.3136). From the sample observed, I must continue to assume that there is no significant difference in the proportion of customers with children in their vehicle that order from the drive-thru and who order from the inside dining area.

Although the sample that was observed did not provide any evidence to reject the null hypothesis, different results may have been found if the sampling process was changed slightly. If there had been a more definite way of cutting off the age of the children that were considered to be “children” for the sample, more accurate results would have been found. Also, because the subjects for the sample used to compute the test of significance and the confidence interval were randomly selected from a larger sample, a significant difference in the proportions may have been found if different subjects were randomly selected. Even though there was not a significant difference found in the proportions, if more accurate sampling methods are used, different results may be found.
Parking Lot Diagram

Exit Entrance

Random Digits Table Used For Selecting Samples

Column

Row 1 2 3 4 5 6 7 8 9 10

1 57245 39666 18545 50534 57654 25519 35477 71309 12212 98911

2 42726 58321 59267 72742 53968 63679 54095 56563 09820 86291

3 82768 32694 62828 19097 09877 32093 23518 08654 64815 19894

4 97742 58918 33317 34192 06286 39824 74264 01941 95810 26247

5 48332 38634 20510 09198 56256 04431 22753 20944 95319 29515

6 26700 40484 28341 25428 08806 98858 04816 16317 94928 05512

7 66156 16407 57395 86230 47495 13908 97015 58225 82255 01956

8 64062 10061 01923 29260 32771 71002 58132 58646 69089 63694

9 24713 95591 26970 37647 26282 89759 69034 55281 64853 50837

10 90417 18344 22436 77006 87841 94322 45526 38145 86554 42733

11 78886 86557 11295 07253 29289 44814 58898 36929 66839 81250

12 39681 54696 38482 48217 73598 93649 92705 34912 18981 74299

13 38265 45196 31143 82190 27279 79883 20219 38823 84543 22119

14 34270 41885 00079 63600 59152 10670 27951 77830 05368 58315

15 73869 34748 75787 88844 89522 71436 04166 06246 20952 56808

16 21732 36017 69149 70330 90500 73110 92908 55789 73450 68282

17 72583 49811 67519 98476 97889 37112 94963 91140 24571 23446

18 72678 49483 57039 18420 74773 16869 72077 27720 14058 66743

19 88572 01294 14117 56884 77107 53023 02243 26415 52233 12818

20 82868 59988 42323 96542 96733 00056 74887 21914 48300 96404

21 09949 56572 28104 64281 01217 76250 39511 19059 85172 35273

22 41942 91440 81609 38147 59406 88491 18079 29786 81499 85390

23 46777 74928 91290 55022 56629 01335 61379 71134 86187 70717

24 58280 17867 07990 85055 55279 83390 37598 93350 05666 55402

25 87042 55080 76185 19947 79551 77594 87381 99430 44251 30896

26 72183 39856 94385 55160 50680 68443 95437 74302 06204 71004

27 76768 16066 94109 90685 92058 81744 99133 36354 34292 90092

28 21703 64616 03431 47610 31968 61593 36259 70600 53491 95542

29 78269 12087 32204 81177 30333 83630 06026 89308 94179 54907

30 49285 16579 22109 63651 34778 28631 27285 95751 91704 59819

31 90016 10303 81862 41351 88681 76632 15336 91955 38436 43892

32 63651 93677 08027 80384 71134 79937 23322 10577 21413 86688

33 02780 37186 74076 33376 03782 64199 77333 12812 78027 89926

34 49414 09022 38644 53038 34634 36565 01984 88477 83879 60943

35 53861 74046 04778 08365 83104 79004 88335 54047 99675 41864

36 78677 55123 73447 00158 61482 02808 83475 59932 19044 27318

37 74550 84403 56850 83780 88847 65591 03859 58670 60057 25225

38 22866 64152 35023 35701 98228 53388 82321 34392 09589 97340

39 17601 32926 06120 27626 48687 42885 25858 53920 95764 84716

40 20862 64222 96951 19524 15866 52508 03763 98033 87268 71167

41 71490 83428 78903 81931 24345 37331 03971 38118 01065 36010

42 21050 12825 28217 99510 86900 09987 91244 06520 81108 87266

43 91632 96199 54191 77480 33049 00849 96668 65865 25164 98330

44 46988 84607 55711 43874 26532 76307 38846 55961 83227 16069

45 72200 24023 55848 09162 44976 15663 34697 83365 82930 63392

46 88621 25822 78463 72191 00625 85945 72522 29613 46473 51177

47 15384 03326 32091 20199 70046 64343 20566 79050 43837 15831

48 46499 94631 17985 09369 19009 51848 58794 48921 22845 55264

49 13520 96795 79714 66338 79836 44430 89290 06167 69090 29476

50 24323 00280 73922 43447 00319 92899 75411 91840 39594 17621

51 99090 55543 87734 80685 74261 70848 87196 59085 28471 74971

52 97585 33311 68919 33189 49987 24081 79404 45363 46920 94760

53 97622 85282 58594 83977 25002 39124 58350 67845 17771 58031

54 24260 21646 75111 41560 90082 57613 93807 04060 94811 60124

55 65250 83876 34806 08796 53719 94310 94363 55289 81226 18190

56 45817 37470 73508 84200 73933 80187 26207 69917 58064 95000

57 48898 28088 77723 81458 18981 35389 17199 85718 18019 66290

58 23900 87304 91349 27541 42047 23002 47976 99586 96453 06861

59 38635 66539 55139 56894 01608 05068 21910 41858 15382 98701

60 58095 49005 59108 12315 35856 19651 55545 79711 42424 67008

61 76474 40345 47744 45224 42903 86698 09851 87819 81523 34272

62 03535 70021 61645 84268 65636 94414 06266 12237 43147 16894

63 14364 82782 07176 53522 06834 46016 42758 04753 00023 15300

64 91751 29817 90578 31800 13393 35965 41128 92983 61660 50106

65 56151 59329 22926 66357 41724 68645 04327 27543 18723 11957

66 57881 15295 43246 47103 15977 84216 78875 06677 77219 50803

67 36126 70899 51669 79958 93311 62555 70694 16626 35623 18758

68 73389 33283 66929 73444 31434 10263 16868 74346 84838 82770

69 77383 40683 84063 45412 21358 84024 88935 77583 33522 53090

70 62798 96248 60474 36149 21187 23194 03696 74445 54525 12869

71 12283 00561 29955 05775 34520 47217 26059 35414 65998 49766

72 78433 49762 41177 80949 32843 64714 40450 15064 11389 78409

73 26348 29480 65497 34615 12888 19977 17597 25914 36394 79315

74 26078 36705 83043 61592 12459 61255 40550 59892 66163 97848

75 40115 70829 00654 12791 85668 19015 82785 92889 35041 18949

76 81560 62666 77627 09123 63484 49481 60451 88073 71000 63511

77 34074 51484 59356 20301 22365 95862 46995 26284 45273 35706

78 42176 81350 05941 09754 16987 98248 90319 33116 39120 34765

79 63288 62381 58461 13225 57138 19619 30877 82640 24888 02600

80 88820 33240 78977 98928 41160 29671 33299 95592 38493 05321

81 63532 20433 25690 09557 90207 95808 57383 68622 13359 25371

82 39033 68857 74705 91718 77485 32496 30737 28551 69056 95615

83 46964 90715 01804 14953 97658 71613 90353 78189 03195 73795

84 03528 92683 29740 31679 22941 92131 69021 21325 70930 19548

85 67027 36641 74347 54500 80074 94364 10164 99309 66272 24925

86 65462 73352 17392 09552 74361 46123 13020 63169 98318 91666

87 55797 95254 84279 88885 65569 96791 66118 05817 17867 88254

88 58697 56009 20438 06653 93978 51961 97609 97367 02795 04718

89 97876 76551 19215 87623 55326 85282 86292 18328 55016 84126

90 72443 02607 13183 06156 76680 62398 79369 77374 78292 41027

91 96152 80526 62087 12197 59252 68312 39759 63535 23675 47358

92 10277 64926 33378 48335 35488 47577 85954 97588 75873 31350

93 77557 25011 86663 97410 99845 42709 48407 63841 14727 00484

94 68784 85951 54232 30976 48666 15927 73072 00907 76237 56914

95 67778 30262 16944 36130 77604 34923 92336 66565 94490 68039

96 94104 06985 81837 53674 36266 21688 68769 18492 12242 34164

97 70107 17900 53497 71908 18186 59909 00400 53236 23016 70860

98 07847 64852 37719 68837 60757 92158 80433 17687 08916 01706

99 33167 35411 27473 13393 17714 59680 30888 98213 93364 03219

100 84527 88986 01665 23547 74666 25487 34977 59681 38520 57293