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Like any statistical experiment, there may be concerns that come along with it.
For our final project, we tested if Bounty napkins were stronger than the generic Market Basket brand of napkins by seeing how many marbles each brand would hold.
Marbles Held
1. There were about 4 marbles that were smaller than the rest, and we did not weigh each marble to determine their actual mass, so we were not 100% sure if all marbles weighed the same. This could've caused it to take more marbles (or less) to rip through the napkin, than if all marbles had weighed exactly the same.
We chose this topic because we were both genuinely interested in the strength of napkins.
In our case, we ended up having a few concerns that may have slightly affected our data, but judging from the drastic differences in the amount of marbles held by the two different types of napkins, it is safe to assume our data was not affected by much.
2. Every once in a while, the eye dropper would drop out a small amount of excess water onto the napkin, causing it to be extremely difficult to get exactly 10 drops on every napkin. This may have caused some napkins to become weaker than others.
Frequency
3. Our last concern was that sometimes, the marbles would be placed differently on the napkins. The marbles were either dropped or placed onto the napkins, but eventually we caused it to become more consistent with whether or not the marbles were placed or dropped.
Once we have our data, we will perform a significance test to find whether or not Bounty napkins are stronger.
As you can see from the 2 histograms, the Bounty distribution appears to be approximately normal but the Market Basket Distribution is skewed to the right.
...
We will proceed with caution.
In order to determine whether Bounty napkins are actually stronger than generic brand (Market Basket) napkins, we created a two sample t-test in order to test whether the true mean amount of marbles held by Bounty napkins is greater than the true mean amount of marbles held by Market Basket napkins.
First, we unfolded a napkin until it was only 1 layer thick and stretched it across a circular container.
After performing our 2 sample T test, we concluded that Bounty napkins were stronger than generic Market Basket napkins.
Next, we wet the napkin by dropping 10 drops of water from an eyedropper.
If the conditions are met we will perform a two sample t-test for
VS
We want to perform a test of
Bounty was thicker and absorbed water more efficiently than Market Basket.
Then we placed marbles onto the napkin until the marbles ripped through it.
Our degree of freedom is:
df: 30-1 = 29
Overall, it is worth it to spend the extra money and buy Bounty napkins and Bounty really is the quicker picker upper.
Since our P:value of is less than our significance level of a=.05, we reject our null hypothesis, and conclude that this experiment provides evidence that the true mean amount of marbles held by Bounty napkins with 10 drops of water is greater than the true mean amount of marbles held by Market Basket napkins with 10 drops of water.
Pure Beauty
Josh's Arm
To find the P:value, we plugged in our t-score of 14.66869, our upper bound of 1,000, and our degrees of freedom of 29 into the tcdf command on our graphing calculator: tcdf(14.66869, 1000, 29)
We performed 30 trials of this test for both Bounty and Market Basket brand, and recorded how many marbles it took to rip through each napkin.
Marbles
Data
Dropper
Napkins