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The conditions are met, so we can continue our test.

Is Bounty really the Quicker Picker Upper?

By: David Caizzi and Josh Thomas

Introduction

Data analysis

Concerns

Bounty vs Market Basket

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

  • As you can see from the side by side boxplots, everything about the Bounty data is larger than the Market Basket data.
  • The median, Q1, Q3, the range, and the IQR are larger

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.

Bounty

Market Basket

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.

Conclusion

Obtaining the data:

Performing Our Test

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.

Step 2: Plan

Step 1: State

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

Normal

Independent

Random

  • is the true mean amount of marbles that a Bounty napkin can hold with 10 drops of water on it
  • is the true mean amount of marbles that a Market Basket napkin can hold with 10 drops of water on it.

We want to perform a test of

Since our sample sizes for both Bounty napkins and Market Basket napkins were at least 30, the Central Limit Theorem applies, so we can say that our distribution is approximately normal.

The strengths of each napkin are independent from each other, so the napkins can be seen as independent.

The 30 Bounty napkins and 30 Market Basket napkins were randomly placed on the shelves at the store, meaning that they were also purchased randomly.

Bounty was thicker and absorbed water more efficiently than Market Basket.

We will test at the a= .05 significance level.

Then we placed marbles onto the napkin until the marbles ripped through it.

Step 3: Do

Step 4: Conclude

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.

Our P:value was calculated to be:

Marbles

Data

Dropper

Napkins

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