invest_3ed.pdf

# Level x specify the number of successes or p ˆ n s

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iscamonepropztest(observed, n, hypothesized, alternative, conf.level) x Specify the number of successes or p ˆ , n , S 0 , alternative, and confidence level (in that order) - Remember to adjust inputs if performing the Adjusted Wald interval x For the alternative, choose “two.sided” or “less” or “greater” (with the quotes) x If no alternative is specified, be sure to label the confidence level (conf.level) In Minitab: Stat > Basic Statistics > One Proportion x Specify a column of data or the Summarized data (sample count and sample size) x Check the box if you want to perform a hypothesis test x Under Options use the Method pull-down menu to select Normal approximation , set the Confidence level, and/or specify the direction of the alternative - Changing the method here gives you the calculations using the Central Limit Theorem - Use a two-sided alternative to get a two-sided confidence interval - Remember to consider the Adjusted Wald (Plus Four) interval procedure May give you a warning message if the sample size condition is not met (but ignore if Adjusted Wald) p ˆ p ˆ

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Chance/Rossman, 2015 ISCAM III Investigation 1.17 117 Investigation 1.17: Cat Households A national survey of over 47,000 households in 2007 found that 32.4% of American households own a pet cat or vice versa ( 2007 U.S. Pet Ownership & Demographics Sourcebook ) . (a) Identify the observational units and variable of interest. Observational units: Variable: (b) Is 32.4% a parameter or a statistic? Indicate the symbol used to represent it. (c) Conduct a test of whether the sample data provide evidence that the population proportion who own a pet cat differs from one-third. State the hypotheses, and report the test statistic and p-value. State your test decision at the D = 0.01 level, and summarize your conclusion in the context of this study. (d) Explain why the p-value turns out to be so very small, when the sample proportion of households with a cat seems to be quite close to one-third. (e) Produce a 99% confidence interval (CI) for the population proportion who own a pet cat. Interpret this interval. (f) Is the confidence interval consistent with the test decision? Explain. (g) Do the sample data provide very strong evidence that the population proportion who own a pet cat is not one-third? Explain whether the p-value or the CI helps you to decide. (h) Do the sample data provide strong evidence that the population proportion who own a pet cat is very different from one-third? Explain whether the p-value or the CI helps you to decide.
Chance/Rossman, 2015 ISCAM III Investigation 1.18 118 Discussion: Keep in mind the difference between statistical significance and practical significance . With large sample sizes, sample proportions will vary little from sample to sample, and so even small differences (that may seem minor to most of us) will be statistically significant. Saying that a sample result is unlikely to happen by chance (and therefore is statistically significant) is not the same as saying the result is important or even noteworthy (practically significant), depending on the context involved.

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