\"It\'s clearly the economy,\" says Kendra Phillips of Awesome Vet Advisers, in

Question

"It's clearly the economy," says Kendra Phillips of Awesome Vet Advisers, in Colorado Springs, CO. She presented the findings at the vets association's national meeting in San Diego (in August 2012). "The percentage of households that owned at least one pet was down 2.4%." That's 2.8 million households that became petless. "It's a significant number," she says.

In 2012, 36.5% of U.S. households reported owning a dog. This is a drop from 37.2% reported in 2007. Ms. Phillips feels that is "a significant number," but her friend, Alyssa, wondered whether this drop in dog ownership statistically significant.

Alyssa noticed that the data that Kendra was quoting from was based on a survey of 100,000 households. Alyssa calculated the following confidence interval: 0.372 - (1.96 x SQRT (0.372 x 0.628 / 100,000) 0.372 + (1.96 x SQRT (0.372 x 0.628 / 100,000) --> 0.369 0.375 .

What should Alyssa conclude about whether the drop from 37.2% to 36.5% is statistically significant?

References:

Pet ownership declines, but more households loyal to dogs.
U.S. Pet Ownership Statistics.

Explanation / Answer

Confidence interval is 0.369 0.375.

The confidence interval still contain 0.372 shows that 37.2% is still a plausible value of proportion. The drop from 37.2% to 36.5% is NOT statistically significant.

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