Question

Strong paper towels In commercials for Bounty paper towels, the manufacturer claims that they are the “quicker picker-upper,” but are they also the stronger picker-upper? Two of Mr. Tabor’s statistics students, Wesley and Maverick, decided to find out. They selected a random sample of 30 Bounty paper towels and a random sample of 30 generic paper towels and measured their strength when wet. To do this, they uniformly soaked each paper towel with 4 ounces of water, held two opposite edges of the paper towel, and counted how many quarters each paper towel could hold until ripping, alternating brands. The data are displayed in the relative frequency histograms. Compare the distributions

Part (a). Would it be appropriate to use frequency histograms instead of relative frequency histograms in this setting? Explain why or why not.

Part (b). Compare the distributions of number of quarters until breaking for the two paper towel brands

Short answer

Part (a) Yes

Part (b)

The bounty distribution is skewed to the left, while the generic distribution is roughly symmetric.

There do not appear to be any outliers in either distribution.

The center of the generic distribution is approximately 90 quarters, while the center of the bounty distribution is approximately 120 quarters.

Both distributions appear to have roughly the same spread.

Step-by-step solution

Part (a) Step 1 Given information. 

Strong paper towels In commercials for Bounty paper towels, the manufacturer claims that they are the “quicker picker-upper,” but are they also the stronger picker-upper. The data are displayed in the relative frequency histograms.

Part (a) Step 2  In this case, would frequency histograms be preferable to relative frequency histograms

Yes, because the two histograms are based on the same number of data values, frequency histograms should be used instead of relative frequency histograms (as there are 30 Bounty paper towels and 30 generic paper towels in the two samples). Because these two histograms are based on the same number of data values, we can compare the frequency histograms.

As a result;

Yes

Part (b) Step 1 The number of quarters until breaking distributions for the two paper towel brands

Because the highest bars are roughly in the middle of the distribution, the generic distribution is roughly symmetric. Because the highest bars in the histograms are to the right, with a tail of smaller bars to the left, the bounty distribution is skewed to the left.

Because there are no gaps in the histograms, neither distribution appears to have any outliers.

The center of the generic distribution is approximately 90 quarters, as expected from the highest bar in the histogram. Similarly, we anticipate that the center of the bounty distribution will be around 120 quarters.

As a results:

The bounty distribution is skewed to the left, while the generic distribution is roughly symmetric.

There do not appear to be any outliers in either distribution.

The center of the generic distribution is approximately 90 quarters, while the center of the bounty distribution is approximately 120 quarters.

Both distributions appear to have roughly the same spread.