\"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, 30.4% of U.S. households reported owning a cat. This is a drop from 32.4% reported in 2007. Ms. Phillips feels that is "a significant number," but her friend, Alyssa, wondered whether this drop in cat ownership statistically significant. Alyssa noticed that the data that Kendra was quoting from was based on a survey of 10,000 households. Alyssa calculated the following confidence interval: 0.324 - (1.96 x SQRT (0.324 x 0.676 / 10,000) 0.324 + (1.96 x SQRT (0.324 x 0.676 / 10,000) --> 0.3148 0.3332 . What should Alyssa conclude about whether the drop from 32.4% to 30.4% is statistically significant?

Explanation / Answer

A confidence interval is an interval of values that is likely to "capture" the unknown value of a population parameter of interest, such as the true population mean, , or the true difference, d. ... Then we would expect 95%, or 950, of theseconfidence intervals to contain the true population parameter.

Your decision can also be based on the confidence interval (or bound) calculated using the same . For example, the decision for a test at the 0.05 level of significance can be based on the 95% confidence interval:

Here,

Notice that this 95% confidence interval goes from 0.3148 up to 0.3332. Since the interval does not contain 0, we see that the difference seen in this study was "significant."

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