Conversions from Human Years to Dog Years

Traditionally, the conversion between dog ages and human ages has been thought to be seven dog years for every human year.

In order to test whether this relationship still holds, I conducted a survey of the lifespans of pet dogs. In this problem you should assume that the true standard deviation of the lifespans of dogs is 2 years.

According to the 1997 World Almanac and Book of Facts, life expectancy for humans is 75.8 years. That would be 75.8 / 7 = 10.8 in dog years, if the conversion is really seven to one.

Here are the data for 19 lifespans of pet dogs: 


 9 13 10 15 14 13 11 14 12 9 12 12 8 15 16 11 13 15 11
  1. Write down the null and alternative hypotheses, using appropriate statistical notation.

  2. Calculate the test statistic, and compute the p-value.

  3. Write a conclusion in the context of the problem.

  4. What conversion between dog ages and human ages should be used, assuming that you believe that seven to one is wrong?

  5. Do dogs seem to live longer or shorter lives than the seven to one conversion would indicate? Can you think of reasons for the discrepency?
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    Last modified by Tom Short