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School Lunch Choices

School Lunch Choices. Justin Lee, Sagar Patel, Kyle Knight. The Topic. We chose to research the meal choices CB South students make. Are females more health conscience than males? What is the average amount spent on lunch? What percent of students buy fries?. Background.

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School Lunch Choices

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  1. School Lunch Choices Justin Lee, Sagar Patel, Kyle Knight

  2. The Topic We chose to research the meal choices CB South students make. Are females more health conscience than males? What is the average amount spent on lunch? What percent of students buy fries?

  3. Background • Our School Lunch • Divided into A, B, C, D lunch. • Requires student ID numbers to buy lunch. • School lunch with Aramark started recently. • Aramark • A company that is in charged with providing lunches to Central Bucks South High School. • A leading food industry that provides food services, facilities management, and uniform and career apparel to health care institutions, universities, and school districts. • Teenager Lunches • About 25 billion pounds of potatoes are consumed by teenagers every year. • Fruits and healthy vegetables are neglected. • Soft drink consumption is still high.

  4. Data collection Systematic random sample. Observed every third person. After five subjects recorded, moved to a new line. Repeated this process for all four lunches for two days.

  5. Procedure After collecting data we created a histogram, bar chart, and a contingency table using the data. We then created two intervals and preformed two tests. We used the results to make conclusions about CB South school lunch buyers.

  6. Exploratory Data Analysis The histogram is unimodal and roughly symmetric. The histogram is centered at about $3.00; the mean and median are very similar. The standard deviation is $1.19743 and the IQR is $1.25, so it has wide spread. In fact, there are a couple outliers on either side, as seen above in the boxplot. Conclusion: The distribution of transactions can be approximated by a normal model centered at $3.09. Considering that a meal deal costs $2.50, the majority of people have transactions that exceed the price of a basic meal deal.

  7. Exploratory Analysis Conclusion: Milk is the most popular overall and about 45% of males and 39% of females bought milk. Also, no females bought juice and milk. It seems that both genders prefer buying milk and not juice. This may because milk is covered under the meal deal and juice is not – it is counted as a side. Milk is the most popular for both genders with 19 for females and 38 for males No females bought both juice and milk About one-fifth of the transactions involve no drink 45% of males bought milk, while 39% of females sampled bought milk

  8. Exploratory Data Analysis Fries: 61% of purchases included fries Beverage: 43% of transactions were milk Vegetable or fruit: 17% Meal deal: 58 % of transactions qualified as meal deals Sample: 63% of subjects were male The majority of males bought fries while the majority of females did not The majority of males bought meals deals while the majority of females did not Conclusion: The majority of our subjects were male and most subjects bought fries and no fruit or vegetable. The majority of males bought either fries or meal deals while the majority of females did not.

  9. Confidence Interval of Average Transaction Total Conditions: SRS: Systematic random sample assumed to be representative. Population ≥ 10n: All students that buy lunch at CB South are ≥ 1,330 Normal population: n=133 n ≥ 30 or n ≥ 30 Conditions met for Student’s t-distribution 1-sample t interval.

  10. Confidence Interval of Average Transaction Total n=133 Confidence=95% 3.09436 ± t*(1.19743/11.5326) (2.889, 3.2997) We are 95% confident that the average amount spent on school lunches by CB South students is between $2.89 and $3.30.

  11. Interval of Proportion of Students Who Buy Fries • Conditions: • SRS: Systematic random sample assumed to be representative. • np ̂ and nq ̂ >10: • 133(.60902)=80 >10 133(.39098)=52 >10 • Population ≥ 10n: All students that buy lunch at CB South are ≥ 1,330 • Conditions met for normal distribution 1 prop z interval.

  12. Interval of Proportion of Students Who Buy Fries .60902 ± z*(.04231) (0.53609, 0.69195) We are 95% confident that the true proportion of CB South students who buy fries is between 53.6% and 69.2%.

  13. Transaction Total And Gender(2-Sample t-test) • Conditions: •  2 independent SRS: Female systematic random sample independent of male sample. • Pop1>10n1: All CB South females that buy lunch >490. • Pop2>10n2: All CB South males that buy lunch > 840. • 2 Normal populations • Or n1 and n2> 30: n1=49 >30 n2 =84 >30. • Conditions met for Student’s t distribution 2 sample t test.

  14. Transaction Total And Gender(2-Sample t-test) t= -1.2176 df=103.3681 P(t<-1.2176)=.1131 We fail to reject the Ho because our P-value of .1131 is greater than alpha=.05. We have sufficient evidence to conclude that the average amount females spend on lunch is equal to the average amount males spend on lunch.

  15. Chi Square Test for Independence Observed Expected No Yes F 40.526 8.4737 M 69.474 14.526 Conditions: Categorical Data: Gender and fruit or vegetable selection are categorical. SRS: Assumed to be representative. All Expected counts >5 Conditions met for a Chi-Square distribution and a Chi-Square test of Independence.

  16. Chi Square Test for Independence Ho: Gender and Fruit or vegetable choice are independent. Ha: Gender and Fruit or vegetable choice are dependent. =(37-40.526)^2 + (12-8.4737)^2 +…= X^2=2.809 40.526 8.4737 df=1 P( X^2>2.809)=.09372 X^2=2.809 We reject the Ho at the significance level of .1 because our P-value is less than alpha of .1. Therefore we have sufficient evidence to conclude that gender and fruit or vegetable choice are dependent.

  17. Conclusions about CB South School Lunch Buyers The average amount CB South students spend on lunch is between $2.89 and $3.30. The majority of those who buy lunch also buy fries (53.6%- 69.2%) The average amount spent on lunch by females and males at CB South is the same. CB South females are more health conscious than males in that they are more likely to purchase a fruit or vegetable side with their lunch than males.

  18. Errors/ Sources of Bias There are different recorders at each lunch. We only collected data for two days, and that there are different options served every day. We also could have differences in agreement regarding what constitutes a fruit (does tomatoes on a salad count, does canned fruit count, does fruit juice count?). Some people may also avoid the line we are recording at because they may be self-conscious about their diet. We found that more males were present in the lunch lines than females. This lack of female data may have affected our results.

  19. Personal Opinions/ Conclusions It was interesting to find the percent of teenagers at CB South who buy fries and the average amount of money that CB South students spend on their lunches. It was difficult for us to collect data because the line was moving fast. Also, lunches were divided to A, B, C, D which made it harder for us to collect data because we had to recruit a friend from C lunch to record data. Putting the data to Fathom was a bit tedious.

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