A dog food company published a special diet for small dogs.

Question

Dog Food Diet Survey Results

A dog food company published a special diet for small dogs. The company conducted a survey of  1,000 dog owners  who each owned a pet belonging to one of four breeds of small dogs. During the survey, all dog owners fed the special diet to their pets for a month. The survey was designed to help the company determine whether dog owners believed that the diet could improve some aspect of their pet's health. The results of that survey are shown in the table below.

Improvement in  
  Beagles   (259 dog owners)  
  Chihuahua   (286 dog owners)  
  Maltese   (224 dog owners)  
  Papillons   (231 dog owners)  
 
  Breath 
 3% 
 1% 
 10% 
 11% 
 
  Coat and skin 
 5% 
 3% 
 13% 
 7% 
 
  Digestion 
 5% 
 4% 
 2% 
 5% 
 
  Energy levels 
 1% 
 2% 
 3% 
 1% 
 
  Firmer stools 
 11% 
 3% 
 19% 
 6% 
 
  Flatulence 
 4% 
 7% 
 11% 
 9% 
 
  No improvement 
 15% 
 17% 
 21% 
 10% 
 
  Other 
 8% 
 12% 
 15% 
 11% 
 
  Resistance to allergies 
 30% 
 28% 
 15% 
 26% 
 
  Uncertain 
 27% 
 13% 
 19% 
 28% 
 
  Weight loss 
 7% 
 9% 
 9% 
 2%

I am unable to add 5 columns below - apologies; so I am adding the table here only - deeply sorry if this is causing issue to anyone:

Dream009 · Answer

I don't agree with experts global solution of 2nd part being true. They are saying of the 20% who find beneficial - how do we know its not seperate pet owners and not the same - this is an assumption

veritatisharum · Answer

can someone please give the solution for this

nottakenname · Answer

Finally i get to be the helpful one here.

Great question. The short answer is that we don't know but it does not matter.

Let’s consider two scenarios, a “best case” and a “worst case” (their labels being completely arbitrary, only serving to indicate that they represent extremes)

Best case scenario, “Resistance to allergies” and “Digestion” is mutually exclusieve, meaning no owner is concerned with both allergies and digestion. Even just looking at the numbers in the two rows, we see that they do not add up to more than 100% so we can confidently say, that exactly 0% of the dog owners who find the diet beneficial for their pet’s resistance to allergies also find it helpful for their pet’s digestion.

Worst case scenario, “Resistance to allergies” and “Digestion” refer to the exact same group of people. Let’s examine each dog breed:

Breed	Allergies	Digestion	Digestion / Allergies
Beagles	5%	30%	17%
Chihuahua	4%	28%	14%
Maltese	2%	15%	13%
Papillons	5%	26%	19%

So even in the worst case scenario no more than 20% the dog owners who find the diet beneficial for their pet’s resistance to allergies also find it helpful for their pet’s digestion.

Hope this helps

dothitmotw · Answer

How did you calculate values under digestion/allergies in the table?

Thank you

Bunuel · Answer

In that solution, those numbers are simply the digestion% divided by the allergies% for each breed. It is a hypothetical worst-case overlap to show the ratio is still under 20%.

agrasan · Answer

Hi  KarishmaB   Bunuel

Could you please explain how "Energy levels of their pets is a concern for only a small proportion of dog owners who were surveyed." is not supported? If I read numbers correctly, they are <12% for all breeds which is a small number. Please let me know where I went wrong.

Bunuel · Answer

The statement is  not supported  because the table shows only the improvement in energy levels, not how many owners were concerned about it. The low percentages of improvement don't mean energy levels weren't a concern. We can't assume that based on the data provided.

Supported	Not Supported	Questions
		A majority of the dog owners believe that the recommended diet could improve some aspect of their pet's health.
		Fewer than 20% of the dog owners who find the diet beneficial for their pet's resistance to allergies also find the diet to be helpful for their pet's digestion.
		Energy levels of their pets is a concern for only a small proportion of dog owners who were surveyed.

A dog food company published a special diet for small dogs.

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Improvement in	Beagles (259 dog owners)	Chihuahua (286 dog owners)	Maltese (224 dog owners)	Papillons (231 dog owners)
Breath	3%	1%	10%	11%
Coat and skin	5%	3%	13%	7%
Digestion	5%	4%	2%	5%
Energy levels	1%	2%	3%	1%
Firmer stools	11%	3%	19%	6%
Flatulence	4%	7%	11%	9%
No improvement	15%	17%	21%	10%
Other	8%	12%	15%	11%
Resistance to allergies	30%	28%	15%	26%
Uncertain	27%	13%	19%	28%
Weight loss	7%	9%	9%	2%

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A dog food company published a special diet for small dogs.

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