Suppose a veterinarian wants to estimate the difference between the proportion o

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 158 randomly selected cat owners and 139 randomly selected dog owners and asks each of them if they are single or married. Her findings are summarized in the table.

Calculate the upper and lower limits (bounds) for a large sample 90% zconfidence interval for the difference in two population proportions, p1p2. 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 Bank

0.068

difference in the proportions of all cat and dog owners

probability is 90%

proportion of dog owners

mean number of cat owners

0.333

0.092

0.097

0.866

0.068

veterinarian can be 90% confident

difference in the mean numbers of cat and dog owners

0.463

0.043

0.048

0.089

mean number of dog owners

difference in the proportions of cat and dog owners in the samples

0.039

0.415

0.107

0.156

proportion of cat owners

0.335

0.118

0.680

0.118

lower limit =

upper limit =

Population Population
description Sample
size Number
of successes Sample
proportion 1 cat owners n1=158 x1=63 p 1=0.39873 2 dog owners n2=139 x2=52 p 2=0.37410

Explanation / Answer

Sample   X    N Sample p
1       63 158 0.398734
2       52 139 0.374101

Difference = p (1) - p (2)
Estimate for difference: 0.0246335
90% CI for difference: (-0.0684412, 0.117708)
Test for difference = 0 (vs 0): Z = 0.43 P-Value = 0.664

Fisher’s exact test: P-Value = 0.721

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