Campbell’s Chicken NoodleSoup Project

What’s really in the bowl??

A Compilation of the Best of the Bestfrom STA 2023 Groups

Fall 2009-2010

Campbell’s Chicken Noodle Soup ProjectWhat’s In the Bowl

Abstract 1—Tiffany M, Missy F, Jimmie S

A study was conducted by two Elementary Stats classes in an attempt to dispute the claim touted by Campbell’s Chicken Noodle Soup that there are 32 feet of noodles in every can of soup. We randomly sampled 33 cans of soup with a sample mean length of 396.576 inches (33.048 feet), p-value of 0.0475, alpha = 0.05, therefore reject Ho = 384 inches and believe Ha not = 384 inches. The 95% Confidence interval is 384.14947 < u < 409.00205. According to the sample data, Campbell’s Chicken Noodle Soup has significantly more than 32 feet of noodles in every can.

Abstract 2—Bethany M, Gabrielle H

We tested the claim that Campbell’s Chicken Noodle Soup contained the advertised 384 in. of noodles. We collected our data by taking a random sample of 33 cans and laying the noodles in each can in lines for measurement. We then used the appropriate statistics, visual aids, and tests to interpret and illustrate our data. We concluded that the population mean length of noodles is not 384 inches, the original claim Campbell’s Chicken Noodle Soup advertised (p=.0435) . The confidence interval shows that it was greater.

Introduction 1—Meleny P, Israa Q

Campbell’s advertisements claim that every can of their Chicken Noodle Soup contains 32 feet (384 inches) which sounds like a shocking claim at first. We will be looking into this claim made by Campbell’s to determine if it is a false advertisement. When a company advertises their product their intentions is to grasp the consumer’s eye so that they will buy their project. As Campbell’s have advertise this 32 feet (384 inches) of noodles in their 10 ½ ounces cans it brings to many people’s attention that what if they could be falsely advertising their product so that they could have more sales. By doing this project this question will be answered.

We first will explain the sampling process and critique the experiment to determine whether it was effective. Then discuss the results that we have found. Then briefly write a conclusion about our findings and also mention any suggestions that may be helpful for future students when doing this project.

Our paper is organized into sections, first is methods in which we explain our sampling methods and critiques, followed by our results in which we examine the data and give our findings, finally we end this paper in a conclusion where you can expect to find a summary of our results and comments about Campbell’s advertisement

Introduction 2—Gina B, Michael S, Gazmend S

We are a group of students at SPC in St. Petersburg, FL interested in knowing if the claim made by the Campbell’s soup company that every can of Chicken Noodle soup it produces contain 32 feet of fresh noodles is true or false.

The following report will describe the manner in which we put the proposed question “Is there or is there not 32 feet of egg noodles in every can of Campbell’s Chicken noodle soup,” to the test. First we will describe to you how our data was collected. Then we will explain our methods of statistically analyzing the data collected. And ultimately we will come to a conclusion as to if we agree with this claim or not.

Introduction 3—Amy K, Paul P, Jeremy B

Crossover Studies

Two informal studies which tested the claim that Campbell’s Chicken Noodle Soup contains thirty-two feet of noodles per can were found. The analyses were conducted by Allen, Washington’s KING 5 news station http://www.king5.com/news/consumer/Let-Jesse-Buy-It-Noodles-67875162.html and South Bend, Indiana’s WNDU http://www.wndu.com/specialfeatures/headlines/69612992.html

Methods 1— Amy K, Paul P, Jeremy B

Students from two Elementary Statistics classes (STA 2023-1388 and STA 2023-1306) were subdivided into small groups containing two to three students. Each group was then responsible for purchasing two cans of Campbell’s Chicken Noodle soup, measuring the total noodle length of each can, and documenting the data. Most groups performed their measurements at the same location and time as their classmates. Those who elected to perform measurements and data collection independently were responsible for providing photo documentation of their results. Elementary Statistics class STA 2023-1388 obtained their measurements first, and created a short video documentary which set the protocol for the students of STA 2023-1306. The video document is available for viewing at http://www.youtube.com/watch?v=kXX6-xctc1E

Methods 2—Amy J, Bill W

In the fall 2009 statistic class, there were 20 groups of students with between 2-3 members in each group. Of the 20 groups, there were 39 possible samples with 6 samples not being reported by their respective group. In all total, there were a total of 33 samples taken.

The technique that was utilized was the following:1. The work area was prepared with plastic tarps.2. Each measuring area was equipped with a tape measure locked at 10 feet. 3. Each can was opened individually and the chicken broth was strained from the noodles with a

colander. 4. Working in teams of two, each noodle was placed end to end next to the tape measure.5. Every effort is made to keep the noodles straight and aligned.6.

Pictures of team members completing the measurement of data

Methods 3—Hahn L, Tan L, Philip C

To verify this claim, we purchased 33 cans of the noodle soup from various grocery stores in and around the St. Petersburg area. We opened the cans and strained the contents leaving only the noodles and we laid them out end to end as evenly as possible on a huge plastic mat alongside measuring tapes. We then measured the combined length of the noodles per can and loaded the data onto the Data Desk computer application for analysis.

Although the use of the plastic mat has proven to be effective in containing our mess in the classroom, it also presented a little bit of a problem. It probably would have been more helpful if we laid the noodles on an even surface, like the floor, instead of a non-stationary and an uneven surface that the plastic offered.

Also, the use of the measuring tapes was convenient but yard sticks probably would have been better in measuring the noodles because the measuring tapes had the tendency to bend which in turn could compromise the accuracy of our data.

Results and Discussion

Sample Statistics—Compiled from several groups

The average length of the noodles in each can of Campbell's Noodle Soup is 33.05 feet (396.58 in.).Standard deviation is 2.92 feet or 35.04 inches.

The measures of position are displayed on the boxplot above.

The median length is 32.58 feet (391 in.), which means half of the noodles had a length above 32.58 ft and the other half had a length below 32.58 ft.

The middle 50% of the length of the noodles were between 31.38 ft and 34.94 ft. for an interquartile range of 3.56 ft or 42.75 inches.

The lower quartile for all the noodles is 31.38 ft indicating that 25% of the noodles measured less than 31.38 ft and 75% of the noodles measured above 31.38 ft. The upper quartile is 34.94 ft, indicating that 25% of the noodles measured more than 34.94 ft and 75% scored less than 34.94 ft.

Histogram 1—Ivonne C, Selita V

The histogram distribution of the length in inches is unimodal, symmetric, and essentially normal. There are neither skews nor outliers. Most of the noodle lengths fall between 380 (31.67 feet) and 420 inches (35 feet). The mean is about 397 inches with a standard deviation of about 35. The three standard deviations above the mean would be at 432, 467, and 502 while the three standard deviations below the mean would be 362, 329, 292 inches. As you can see, all of the noodle data falls within the plus or minus three standard deviations from the mean of 397. (Red text added by Dr. E.)

Histogram 2—Jonathan C, Sarah B, Josh W

In the histogram above, we measure the distribution and symmetry to determine if the distribution is skewed. Our graph is unimodal in that it contains one peak where the majority of the noodle lengths are between 380 and 395 inches. The histogram is also relatively symmetric which means there is the same amount of noodle lengths below the peak as there are above it. In shor the distribution model is unimodal and symmetrical, and there are no gaps or outliers.

Data Analysis

Since sigma (the population mean) is not known, a t-test for a single mean most be conducted. For this to be the proper test certain assumptions must be meet.

Assumptions 1—Aida, Bea, Darren, Kyle, Scott

Assumption 1: Sigma is not knownATSG doesn’t know the standard deviation of the populaiton mean. This assumption is met.

Assumption 2: The parent population is essentially normalStatistical data was analyised using a histogram to ensure the parent population was essential normal (fig 2). The hisogram of the samples are unimodal, symmetrical, not skewed and contains no outliers. The parent population is essential normal and this assumption is met. (See scatterplot above.)

Assumption 3: The sample is random

33 cans were randomly supplied by the Campbell Soup Company. Cans were received from each plant in the USA. This assumption is met.

Assumption 4: The sample values are mutually independentEach measurement and each can did not have an impact on the measurement results of each other. This assumption is met.

Assumption 5: The sample is not to large. The sample is less than 10% of the population as only 33 cans are measured. This assumption is met.

Assumptions 2—Khaliunaa G, Uyanga G

Since we have the data, we will use data desk hypothesis testing and confidence interval. Before the hypothesis testing or confidence interval, we must see whether or not the assumptions have been met. We will use t-distribution,

1. The population standard deviation sigma is not known and sample standard deviation s is used as an estimate. (In our case, the population standard deviation is not known and sample standard deviation s=35.0446 inches or 2.92038 feet is used as an estimate)

2. The parent population is essentially normal (The histogram of the variable Noodle Length is unimodal and symmetric which indicates that the parent population is essentially normal)

3. The sample is random (33 cans of soups were randomly selected by each group)4. The sample values are mutually independent where one outcome does not affect another. (The sample

values are independent because the outcome of one can of soup will not affect another.)5. The sample size is not too large: The sample size is less than 10% of population size. (The sample of 33

cans is definitely less than 10% of the population size.)

All the assumptions have been met, therefore we use t-distribution.

Hypothesis Testing 1—Jeremy B, Amy K, Paul P

A two-tailed hypothesis test was created which would determine whether the population mean length of noodles per can of Campbell’s Chicken Noodle soup differed from thirty two feet, the noodle length which the Campbell Soup Company states can be found in every can of Campbell’s Chicken Noodle soup.

The model, Ho: μ=32 states that there are 32 feet in every can of Campbell’s Chicken Noodle soup. The claim, Ha: μ = < or > 32 was tested. A significance level of 0.05 was used to assess the probability.

The probability value obtained from the hypothesis test was .048, or 4.8 percent. Although by a small margin, this value falls below the 0.05 significance level, indicating that the sample evidence does support the claim that the population mean length of noodles in Campbell’s Chicken Noodle soup is not 32’. The results of the hypothesis test are summarized above in a DataDesk report. DataDesk is a student resource contained on the ActivStats interactive CD-ROM supplement to the textbook IntroStats (DeVeaux, Velleman, Bock, c. 2009):

Hypothesis Testing 2—Claudia P, Paul H, Selena P

Since our probability value of 0.0475 is less than the Alpha value of 0.05 we conclude we have evidence to disbelieve the model in Ho. Therefore we Reject Ho and believe Ha. (See the table above.)

Reason to disbelieve Ho: µ = 384Reason to believe Ha: µ ≠ 384

We conclude that the sample evidence does support the claim that the population mean length of Campbell’s Chicken Noodle Soup is not 32 feet (384 inches) of fresh noodles in every can as it was advertised.

Confidence Interval 1—Dana N, Tony D

We are 95% confident that the population mean of the Campbell’s Chicken Noodle Soup is between 384.1497 inches (32.01 feet) and 409.00205 inches (34.08 feet). Since the confidence interval is completely above 32 feet, Campbell’s Chicken Noodle Soup has significantly higher than the 32 feet shown in the advertisement.

Confidence Interval 2—Meleny P and Israa Q

We are 95% confident that the population mean is between 384.15 inches (32.013 feet) and 409 inches (34.083 feet). Since 384 inches which is 32 feet is not in the confidence interval, the confidence interval supports the conclusion that the mean for the length of the Noodles is significantly higher than 384 inches (32 feet). (See the table above.)

Conclusion 1—Steve F and Heather G

The Population mean noodle length is not equal to 32 feet or 384 inches. Although the data shows that the population mean is between 384.15 and 409.01 inches. The Campbell’s Soup Company advertising is true to their word that there are 384 inches or 32 feet of noodles in each can. According to the confidence interval they could advertise that there is more than 32 feet of noodles in each can.

Sources of Error Alignment of the individual noodles where imperfect. Keeping each individual noodle straight was problematic.

The experiment was performed under time restraints. The experiment was not preformed in a laboratory. The experiment was not preformed using persist measurement tools. Size shape or diameter of each noodle wasn't considered. The individual weight of each noodle wasn't considered.

See pictures below

Here you see the difficulty in getting the noodle to line up straight. Dexterity was also difficult in handling the slippery noodles.

In this picture the row of noodles are not straight.

Conclusion 2—Paul H, Claudia P, Selena P

In conclusion, our results show that it is far more believable to assume that in Campbell’s Chicken Noodle Soup, there is a slight variation in the actual amount of noodles per can. Although the mean length of noodles per can (in our sample) is actually higher than the claim of 32 feet, which is safe for Campbell’s Soup Company, (who doesn’t want more soup than advertised?) our evidence also suggests that there is a wide range, with the lower 25% of the 33 cans sampled being less than 376.5 inches (31.375 feet.) of noodles measured. For those shoppers unfortunate enough to pick up the wrong can, who knows how little of the actual soup they could buy?