Question

Suppose a veterinarian wants to estimate the difference between the proportion of cat owners who are single and the proportion of dog owners who are single. Of the pet owners that visit any of the veterinarian clinics in her city regularly, she identifies 3872 pet owners that exclusively have cats and 4108 pet owners that exclusively have dogs. From this list of pet owners, she surveys 149 randomly selected cat owners and 126 randomly selected dog owners and asks each of them if they are single or married. Her findings are summarized in the table.

Population	Population description	Sample size	Number of successes	Sample proportion
1	cat owners	?1=149n1=149	?1=68x1=68	?̂ 1=0.45638p^1=0.45638
2	dog owners	?2=126n2=126	?2=54x2=54	?̂ 2=0.42857p^2=0.42857

Calculate the upper and lower limits (bounds) for a large sample 99% ?z‑confidence interval for the difference in two population proportions, ?1−?2p1−p2. Give each of your answers with three decimal places of precision.

Then, complete the following sentence to state the interpretation of the confidence interval.

The                                                                                         that the

who are single is between                                                                                         and

                                                                                         .

Answer 1