Exploration 3.58: Cat Households A survey of 47,000 American households in 2007 found that 32.4% own a pet cat. 1. Is the value 32.4% (or, as a decimal, 0.324) a parameter or a statistic? What symbol would you use to represent this value? 2. Describe (in words) the parameter of interest here. What symbol would you use to represent this parameter 3. Conduct a theory-based significance test of whether the sample data provide strong evidence that less than one-third of all American households owns a pet cat. Specify the null and alternative hypotheses, and calculate the z-score and p-value. Also indicate whether the sample result is statistically significant at the 0.001 level. Summarize your conclusion and explain how it follows from the test. 4. Determine a 99.9% confidence interval for the proportion of all American households that have a pet cat. 5. Explain why this confidence interval is so narrow. Consider the following two possible conclusions: The sample data provide very strong evidence that less than 1/3 of all American households owns a cat. The sample data provide strong evidence that much less than 1/3 of all American households owns a cat 6. Explain the difference between these two statements 7. Which of these two statements can you use a p-value to assess? Which can you use a confidence interval to assess? 8. Which of the two conclusions would you draw from your analysis of these data? Explain your answer. Key idea: Especially with large sample sizes, even a fairly small difference between an observed and hypothesized value can be statistically significant. In such cases a confidence interval for the parameter can help to decide whether the difference is practically important