11_Quiz_Review_Warm_Up_Key

3) Is your big toe longer than your second toe? Does this depend on your age? A random sample of 460 adults in the U.S. was selected and asked to record if their big toe was longer than, shorter than, or the same length as their second toe. The age of each student was also reported. The data are summarized in the table below. χ 2 test for association/independence (because the data comes from one sample) In the test of independence, observational units are collected at random from a population and two categorical variables are observed for each unit. In other words, we are testing two variables contained in a single sample. H 0 : There is no association between toe length and age for the Population of U.S. adults. H a : There is an association between toe length and age for the Population of U.S. adults. 4) An article in the Arizona Daily Star (April 9, 2009) included the following table: Age (years): 18–24 25–34 35–44 45–54 55–64 65+ Total Use online social networks: 137 126 61 38 15 9 386 Do not use online social networks: 46 95 143 160 130 124 698 Total: 183 221 204 198 145 133 1084 Suppose that you decide to analyze these data using a chi-square test. However, without any additional information about how the data were collected, it isn’t possible to know which chi-square test is appropriate. (a) Explain how you know that a goodness-of-fit test is not appropriate for analyzing these data. Since there are either two variables or two or more populations, a goodness-of-fit test is not appropriate. Goodness-of-fit tests are appropriate only when analyzing the distribution of one variable in one population (b) Describe how these data could have been collected so that a test for homogeneity is appropriate. To make a test for homogeneity appropriate, we would need to take six independent random samples, one from each age category, and then ask every person whether or not they use online social networks. Or we could take two independent random samples, one of online social network users and one of people who do not use online social networks, and ask every member of each sample how old they are. (c) Describe how these data could have been collected so that a test for association/independence is appropriate. To make a test for association/independence appropriate, we would take one random sample from the population and ask every member about their age and whether or not they use online social networks. This seems 50- 51+ Total Big Toe longer 85 73 158 Same length 42 44 86 Second Toe longer 100 116 216 Total 227 233 460