Question

A survey found that in a sample of 75 families, 26 owned dogs. A survey done 15 years ago found that in a sample of 60 families, 26 owned dogs. Find the 95% confidence intervals of the true difference in the proportions.

Answer 1

The difference in the proportions of both surveys goes from a maximum of 12.57% to a minimum of 4.76%.

Given that a survey found that in a sample of 75 families, 26 owned dogs, while a survey done 15 years ago found that in a sample of 60 families, 26 owned dogs, to find the 95% confidence intervals of the true difference in the proportions, the following calculation must be performed:

• 75 = 100
• 26 = X
• 26 x 100/75 = X
• 34.66 = X
• 34.66 x 0.95 = 32.93
• 34.66 x 1.05 = 36.40
• 60 = 100
• 26 = X
• 26 x 100/60 = X
• 43.33 = X
• 43.33 x 0.95 = 41.16
• 43.33 x 1.05 = 45.50
• 45.50 - 32.93 = 12.57
• 41.16 - 36.40 = 4.76

Therefore, the difference in the proportions of both surveys goes from a maximum of 12.57% to a minimum of 4.76%.

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