SALT LAKE COMMUNITY COLLEGE
Math 1040 – Term Project
Correlation Study| Microwave Cook Time’s &
Number of Kernels Popped In A Bag of Popcorn.
Anthony Hakala
11/16/2012
Math 1040 – Term Project
Anthony Hakala
11/16/12
Purpose of the Study
As a group we tried to think of populations that could be studied in which we would have more control
over the variables in play, we decided the best course of action would be to study the number of kernels
that pop in a bag of popcorn. We wanted to know is the number of popped kernels related time spent
cooking.
Study Design
To collect our data we used a simple random sample to 1. Determine which brand of popcorn to use and
2. To determine which boxes of popcorn to select off of the shelf. To do this we went into Smiths, taking
note off all the different popcorn brands available. We recorded and numbered each brand of popcorn
that was available for purchase. Using a random number generator we selected the Brand “Act II butter
lover’s” popcorn. Taking note of how many boxes were on the shelf we then numbered them 1-k. using
the random number generator we selected our boxes. Each box contained 6 bags of popcorn, leaving us
with 36 bags of popcorn. We only needed to collect a sample size of 30 bags, so we numbered each bag
and randomly selected 30 from the 36 total bags. From this point each group member took 10 bags and
popped them, we recorded the number of popped kernels and time spent in the microwave.
The Data, Statistics & Graphs
Data Organized into a table
Time Spent in Microwave
0.20
0.24
0.28
0.32
0.36
0.40
0.44
0.48
0.52
0.56
1.00
1.04
1.08
1.12
1.16
# of Kernels
Popped
0
0
0
0
0
0
14
3
25
40
20
23
81
83
85
Time Spent in Microwave
1.20
1.24
1.28
1.32
1.36
1.40
1.44
1.48
1.52
1.56
2.00
2.04
2.08
2.12
2.16
# of Kernels
Popped
127
163
179
233
244
381
389
390
416
393
435
405
415
421
421
Statistics for the First Quantitative Variable:
Mean = 1.1133333
Standard Deviation = 0.6176336
Five Number Summary: Min = 0.2 | Q1 = 0.48 |Median = 1.18 | Q3 = 1.48 | Max = 2.16
Range = 1.96
Mode = None
Outliers = None
Statistics for the Second Quantitative Variable:
Mean = 179.53334
Standard Deviation = 176.32997
Five Number Summary: Min = 0 | Q1 = 14 |Median = 106 | Q3 = 390 | Max = 435
Range = 435
Mode = 421
Outliers = None
Simple linear regression results:
Dependent Variable: # of Kernels Popped
Independent Variable: Time Spent in Microwave
# of Kernels Popped = -109.302666 + 259.43353 Time Spent in Microwave
Sample size: 30
R (correlation coefficient) = 0.9087
Difficulties/Surprises Encountered
Analysis –To be sure of this before starting the experiment I predetermined an alpha level. My Alpha
level was .05. (Meaning I was willing to except being wrong only 5% of the time) Determining the
Degrees of freedom (df) I found that our sample size of n=30 had a (df) of 28. Using the critical value
table found at http://www.gifted.uconn.edu/siegle/research/correlation/alphaleve.htm I was able to find
the intersection between df = 28 and Alpha = .05 which was .361. This intersection of .361 represents the
minimum correlation coefficient r you need to confidently state 95% of the time a relationship will be
found with the 30 bags of popcorn (n) in the population from which they were drawn. If | r | > .361 you
would reject the null hypothesis (There is no relationship) and accept the alternative hypothesis, a
statistically significant relation between time spent cooking in the microwave and number of kernels
popped. In our research we found r = 0.9087 | 0.9087 | > .3610? =True.
Interpretation & Conclusions - From the data collected we can say that we are 95% confident there is a
correlation between time spent in cooking and the number of kernels popped in a bag of popcorn. By
interoperating r= | 0.9087 | > .3610 =True. We see that our correlation coefficient is greater than the
minimum value by .5477, well above what was set as a minimum expectable value; we can also see a
positive regression line in the scatter plot. This combined with a positive r value leads me to believe we
have successfully answered our original question.
Reflective Writing
1. Is the time spent cooking Related to the number of kernels that will pop in a bag of popcorn?
2. The Correlation Coefficient for my groups data = 0.9087
3. The Critical Value of the groups correlation coefficient = .3610
4. From the data collected we can say that we are 95% confident there is a correlation between time
spent in cooking and the number of kernels popped in a bag of popcorn.
5. What Challenges did you face in completing the assignment? How did you address them?
a. When asked what challenges I faced in completing this assignment, I could spend two
pages listing them out. For the sake of conversation I will keep this brief. The assignment
itself did not present me with too many problems; we chose subject matter to study that
seemed fairly straight forward, popping popcorn. The challenges I faced in completing
this task was time. For me time seems to be a constant constraint. Between work, class,
homework (both in stats and other classes) two children, and my wife, I seemed to always
be limited in the amount of time I had to dedicate myself to this project and homework in
general. I over came these limitations by partitioning myself from the things that took me
away from homework and this project, namely my family. By sacrificing the amount of
time I spent with my family and decreasing the amount of sleep I received I was able to
collect my portion of the data, this leads me to my second challenge, communication.
Communicating with my group was also an issue; we never had time before or after class
to talk about the project. We overcame this by electronic communication between text
messaging and email. Once we got into a rhythm it was easier to stay on track with
project goals. Through a collaborative supportive environment my team and I were able
to efficiently and accurately collect data and support each other on the interpretation of
said data.