Examine a likelihood of obtaining the conclusion based on a sample survey.
See solution.
Practice makes perfect
Most of the time, if we want to infer a conclusion about a population we use a sample survey. This is because in most cases it would impossible or impracitcal to survey all members of a population.
After surveying our sample members we get a conclusion about them. However, if we would like to infer a conclusion about the whole population, we should examine the likelihood of obtaining the conclusion based on a sample survey. Assume that we want to test the following conjecture.
Among teenagers, 50 % of them prefer cats over dogs.
Now, let's say that 3 people out of 10 people said that they prefer cats over dogs, which means that in our sample only 30 % of people prefer cats over dogs. In order to estimate the likelihood of obtaining that result we can use a binomial distribution for the number of people out of 10 that prefer cats over dogs, assuming the probability of success to be 50 %.
Using this distribution, we can say that the likelihood that we could have selected a sample in which exactly 3 people surveyed prefer cats over dogs is about 0.12 or 12 %, so this event is not very likely to occur if we are right about our conjecture. This suggests that we should not conclude that 50 % of teenagers prefer cats over dogs.
